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Exercises: Calculus (OpenStax)
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- Page ID 3121
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These are homework exercises to accompany OpenStax's "Calculus" Textmap.
- 1.E: Functions and Graphs (Exercises) These are homework exercises to accompany Chapter 1 of OpenStax's "Calculus" Textmap.
- 2.E: Limits (Exercises) These are homework exercises to accompany Chapter 2 of OpenStax's "Calculus" Textmap.
- 3.E: Derivatives (Exercises) These are homework exercises to accompany Chapter 3 of OpenStax's "Calculus" Textmap.
- 4.E: Applications of Derivatives (Exercises) These are homework exercises to accompany Chapter 4 of OpenStax's "Calculus" Textmap.
- 5.E: Integration (Exercises) These are homework exercises to accompany Chapter 5 of OpenStax's "Calculus" Textmap.
- 6.E: Applications of Integration (Exercises) These are homework exercises to accompany Chapter 6 of OpenStax's "Calculus" Textmap.
- 7.E: Techniques of Integration (Exercises) These are homework exercises to accompany Chapter 7 of OpenStax's "Calculus" Textmap.
- 8.E: Differential Equations (Exercises) These are homework exercises to accompany Chapter 8 of OpenStax's "Calculus" Textmap.
- 9.E: Sequences and Series (Exercises) These are homework exercises to accompany Chapter 9 of OpenStax's "Calculus" Textmap.
- 10.E: Power Series (Exercises) These are homework exercises to accompany Chapter 10 of OpenStax's "Calculus" Textmap.
- 11.E: Parametric Equations and Polar Coordinates (Exercises) These are homework exercises to accompany Chapter 11 of OpenStax's "Calculus" Textmap.
- 12.E: Vectors in Space (Exercises) These are homework exercises to accompany Chapter 12 of OpenStax's "Calculus" Textmap.
- 13.E: Vector-Valued Functions (Exercises) These are homework exercises to accompany Chapter 13 of OpenStax's "Calculus" Textmap.
- 14.E: Differentiation of Functions of Several Variables (Exercise) These are homework exercises to accompany Chapter 14 of OpenStax's "Calculus" Textmap.
- 15.E: Multiple Integration (Exercises) These are homework exercises to accompany Chapter 15 of OpenStax's "Calculus" Textmap.
- 16.E: Vector Calculus (Exercises) These are homework exercises to accompany Chapter 16 of OpenStax's "Calculus" Textmap.
- 17.E: Second-Order Differential Equations (Exercises) These are homework exercises to accompany Chapter 17 of OpenStax's "Calculus" Textmap.
Thumbnail: The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus. (GNU Free Documentation License, Version 1.3 and CC- SA-BY 3.0; Wikipedia).
Math 1a Spring 2020
1a introduction to calculus.
Handouts and Homework
Math 1a, Home | Oliver Knill, [email protected] ,SciCenter 432, (617) 495-5549 | Department of Mathematics | FAS | Canvas | Harvard University
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- Prof. Gilbert Strang
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Calculus online textbook.
First published in 1991 by Wellesley-Cambridge Press , this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor’s Manual and a student Study Guide .
The complete textbook (PDF) is also available as a single file.
Textbook Components
Table of Contents (PDF)
Chapter 0: Highlights of Calculus (PDF)
0.1 Distance and Speed // Height and Slope 0.2 The Changing Slope of \(y=x^2\) and \(y=x^n\) 0.3 The Exponential \(y=e^x\) 0.4 Video Summaries and Practice Problems 0.5 Graphs and Graphing Calculators
Chapter 1: Introduction to Calculus (PDF)
1.1 Velocity and Distance 1.2 Calculus Without Limits 1.3 The Velocity at an Instant 1.4 Circular Motion 1.5 A Review of Trigonometry 1.6 A Thousand Points of Light
Chapter 2: Derivatives (PDF)
2.1 The Derivative of a Function 2.2 Powers and Polynomials 2.3 The Slope and the Tangent Line 2.4 Derivative of the Sine and Cosine 2.5 The Product and Quotient and Power Rules 2.6 Limits 2.7 Continuous Functions
Chapter 3: Applications of the Derivative (PDF)
3.1 Linear Approximation 3.2 Maximum and Minimum Problems 3.3 Second Derivatives: Bending and Acceleration 3.4 Graphs 3.5 Parabolas, Ellipses, and Hyperbolas 3.6 Iterations \(x_{n+1}=F(x_n)\) 3.7 Newton’s Method (and Chaos) 3.8 The Mean Value Theorem and 1’Hôpital’s Rule
Chapter 4: Derivatives by the Chain Rule (PDF)
4.1 The Chain Rule 4.2 Implicit Differentiation and Related Rates 4.3 Inverse Functions and Their Derivatives 4.4 Inverses of Trigonometric Functions
Chapter 5: Integrals (PDF)
5.1 The Idea of an Integral 5.2 Antiderivatives 5.3 Summation versus Integration 5.4 Indefinite Integrals and Substitutions 5.5 The Definite Integral 5.6 Properties of the Integral and Average Value 5.7 The Fundamental Theorem and Its Applications 5.8 Numerical Integration
Chapter 6: Exponentials and Logarithms (PDF)
6.1 An Overview 6.2 The Exponential \(e^x\) 6.3 Growth and Decay in Science and Economics 6.4 Logarithms 6.5 Separable Equations Including the Logistic Equation 6.6 Powers Instead of Exponentials 6.7 Hyperbolic Functions
Chapter 7: Techniques of Integration (PDF)
7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitutions 7.4 Partial Fractions 7.5 Improper Integrals
Chapter 8: Applications of the Integral (PDF)
8.1 Areas and Volumes by Slices 8.2 Length of a Plane Curve 8.3 Area of a Surface of Revolution 8.4 Probability and Calculus 8.5 Masses and Moments 8.6 Force, Work, and Energy
Chapter 9: Polar Coordinates and Complex Numbers (PDF)
9.1 Polar Coordinates 9.2 Polar Equations and Graphs 9.3 Slope, Length, and Area for Polar Curves 9.4 Complex Numbers
Chapter 10: Infinite Series (PDF)
10.1 The Geometric Series 10.2 Convergence Tests: Positive Series 10.3 Convergence Tests: All Series 10.4 The Taylor Series for \(e^x\), \(\sin{x}\), and \(\cos{x}\) 10.5 Power Series
Chapter 11: Vectors and Matrices (PDF)
11.1 Vectors and Dot Products 11.2 Planes and Projections 11.3 Cross Products and Determinants 11.4 Matrices and Linear Equations 11.5 Linear Algebra
Chapter 12: Motion Along a Curve (PDF)
12.1 The Position Vector 12.2 Plane Motion: Projectiles and Cycloids 12.3 Curvature and Normal Vector 12.4 Polar Coordinates and Planetary Motion
Chapter 13: Partial Derivatives (PDF)
13.1 Surface and Level Curves 13.2 Partial Derivatives 13.3 Tangent Planes and Linear Approximations 13.4 Directional Derivatives and Gradients 13.5 The Chain Rule 13.6 Maxima, Minima, and Saddle Points 13.7 Constraints and Lagrange Multipliers
Chapter 14: Multiple Integrals (PDF)
14.1 Double Integrals 14.2 Changing to Better Coordinates 14.3 Triple Integrals 14.4 Cylindrical and Spherical Coordinates
Chapter 15: Vector Calculus (PDF)
15.1 Vector Fields 15.2 Line Integrals 15.3 Green’s Theorem 15.4 Surface Integrals 15.5 The Divergence Theorem 15.6 Stokes’ Theorem and the Curl of F
Chapter 16: Mathematics after Calculus (PDF)
Index (PDF)
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Math 122B - First Semester Calculus and 125 - Calculus I Worksheets
The following is a list of worksheets and other materials related to Math 122B and 125 at the UA. Your instructor might use some of these in class. You may also use any of these materials for practice. The chapter headings refer to Calculus , Sixth Edition by Hughes-Hallett et al. Published by Wiley.
INTRODUCTION
- Tools for Success -A list of resources including tutoring services. website
- Student Survey - A survey to provide background information to an instructor. pdf doc
- Calculator Checklist - A list of calculator skills that are required for Calculus. pdf doc
- Pixels and the calculator screen - An exercise to illustrate the sensitivity of the window settings. pdf doc
- Homework Sample - A few examples to illustrate how homework should be written. pdf doc
CHAPTER 1 - A Library of Functions
- Interesting Graphs - A few equations to graph that have interesting (and hidden) features. pdf doc
- Functions - Properties of functions and the Rule of Four (equations, tables, graphs, and words). pdf doc
- Reading a Position Graph - Answer questions about motion using a position graph. pdf doc
- Reading Graphs - Four graphs and questions using function notation. pdf doc
- Find a Function - Find an example of a function in the media. pdf doc
- INDY 500 - Sketch graphs based on traveling one lap along an oval racetrack. pdf doc
- Farenheit - The relationship between Farenheit and Celsius. pdf doc
- Linear Functions - Applications. pdf doc
- Exponential Functions - Recognizing exponential functions and their properties. pdf doc
- Inverse Functions - Relationships between a function and its inverse. pdf doc
- New Functions From Old - Transformations, compositions, and inverses of functions. pdf doc
- Transformations - A matching exercise using symbolic expressions and tables. pdf doc
- More Transformations - Graphing transformation. pdf doc
- Logarithms - Using logarithms to solve problems. Properties of logas. pdf doc
- Trig Reference Sheet - List of basic identities and rules. pdf doc
- Trig (part I) -Interpreting trig functions and practice with inverses. pdf doc
- Trig (part II) - More practice. pdf doc
- Denise & Chad - An illustration of the effects of changes in amplitude and period. pdf doc
- Polynomials & Rational Functions - Recognizing polynomials and rational functions and their properties. pdf doc
- Power Functions - Use graphs to explore power functions. pdf doc
- Limits and Continuity - Graphical and numerical exercises. pdf doc
- More Continuity - Basics about continuity. pdf doc
CHAPTER 2 - The Derivative
- Introduction to Rates - Introduction to rates of change using position and velocity. pdf doc
- Representations - Symbolic recognition and illustration of rates. Practical interpretation of rates of change using the rule of four. pdf doc
- Practical Example - Reading information about rates from a graph. pdf doc
- Estimation - Estimation using tables and equations. Practice with notation and terminology. pdf doc
- Derivative Graphs - Graphing a derivative function given a graph. pdf doc
- More Derivative Graphs - Matching exercise. pdf doc
- Terminology - Fill in the blank exercise. Practice with terminology pdf doc
- Differentiability - Determine when a function is not differentiable at a point. pdf doc
- More Differentiability - More practice. pdf doc
- Practice - Additional practice covering this section. pdf doc
CHAPTER 3 - Rules For Differentiation
- Product & Quotient Rules - Practice using these rules. pdf doc
- Chain Rule - Practice using this rule. pdf doc
- Base e - Derivation of e using derivatives. pdf doc
- Rules - Practice with tables and derivative rules in symbolic form. pdf doc
- More Practice - More practice using all the derivative rules. pdf doc
- Derivative (&Integral) Rules - A table of derivative and integral rules. pdf doc
CHAPTER 4 - Using the Derivative
- Reading Graphs - Reading information from first and second derivative graphs. pdf doc
- Critical Points Part I - Terminology and characteristics of critical points. pdf doc
- Critical Points Part II - Finding critical points and graphing. pdf doc
- Families of Functions - Finding critical points for families of functions. pdf doc
- More Families of Functions - Finding values of parameters in families of functions. pdf doc
- Optimization Part I - Optimization problems emphasizing geometry. pdf doc
- Optimization Part II - More optimization problems. pdf doc
- Parametric Equations (Circles) - Sketching variations of the standard parametric equations for the unit circle. pdf doc
- Parametric Equations (Misc) - Fun graphs using parametric equations. pdf doc
- Parametric Equations - Finding direction of motion and tangent lines using parametric equations. pdf doc
- Holiday Parametric Equations - Halloween surprise. pdf doc
- L'Hopital's Rule - Practice in recognizing when to use L'Hopital's Rule. pdf doc
- Limit Practice -Additional practice with limits including L'Hopital's Rule. pdf doc
- Introduction to Related Rates - Finding various derivatives using volume of a sphere and surface area of a cylinder. pdf doc
- Related Rates - Additional practice. pdf doc
- More Related Rates -Additional practice. pdf doc
CHAPTER 5 - The Definite Integral
- Intro to Velocity and Area - Relationship between velocity, position, and area. pdf doc
- Representations - Practice with notation, estimation, and interpretations. pdf doc
- Rocket - Application of velocity and position for a model rocket. pdf doc
- Mice - Application of velocity and position for two mice. pdf doc
- Cars - Application of velocity, position, and acceleration of two cars. pdf doc
- Fundamental Theorem Part I - Graphical approach. pdf doc
- Fundamental Theorem Part II - Illustrations and notation. pdf doc
CHAPTER 6 - Constructing Antiderivatives
- Position, Velocity, & Acceleration - Graphical relationships between position, velocity, and acceleration. pdf doc
- Sketching Antiderivatives - Graphing antiderivatives. pdf doc
- Area Between Graphs - Using the Fundamental Theorem to find area between graphs. pdf doc
- Practice - Problems from chapters 5 and 6. pdf doc
- Integration - Recognizing when to use substitution. Integrands look similar. pdf doc
- Substitution - Practice, including definite integrals. pdf doc
- More Substitution - More practice. pdf doc
Math 104: Calculus I – Homework
Section 004 - Spring 2014
- Lecture Videos
Course ID: rimmer21998 For instructions on how to create a login, follow the directions here . All homework will be due at midnight (actually 11:59) on the day listed.
IMAGES
VIDEO
COMMENTS
Differential Equations. Slope Fields. Introduction to Differential Equations. Separable Equations. Exponential Growth and Decay. Free Calculus worksheets created with Infinite Calculus. Printable in convenient PDF format.
Euler's method can be used to approximate solutions of differential equations when finding an explicit solution is too difficult or impossible. This method is based on making a series of "corrections" to the tangent line approximation. (a) The general formula for Euler's method is yn = yn−1 + hF (xn−1, yn−1).
201-103-RE - Calculus 1 WORKSHEET: CONTINUITY 1. For each graph, determine where the function is discontinuous. Justify for each point by: (i) saying which condition fails in the de nition of continuity, and (ii) by mentioning which type of discontinuity it is. (a) (b) 2. For each function, determine the interval(s) of continuity. (a) f(x) = x2 ...
3121. OpenStax. OpenStax. These are homework exercises to accompany OpenStax's "Calculus" Textmap. Thumbnail: The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus.
Introduction to Calculus Spring 2020. Math 1a Spring 2020 1a Introduction to Calculus. Home; Syllabus; Handouts; Q & A; Exam; Data; Exhibit; Quizz; Handouts and Homework ... Collaboration and discussions about the homework is encouraged. Make use of our resources and each other. We have a strict no-late homework submission policy.
Kuta Software - Infinite Calculus Name_____ Area Between Curves Date_____ Period____ For each problem, find the area of the region enclosed by the curves. 1) y = 2x2 − 8x + 10 y = x2 2 − 2x − 1 x = 1 x = 3 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 2) x = 2y2 + 12 ...
2 Chapter 2: Prelude to Calculus Section 2.1: Tangent Lines and Slope Predictors † 5. Find the slope at a and the tangent line at x = 2 of f(x) = 4x¡5. † 7. Find the slope at a and the tangent line at x = 2 of f(x) = 2x2 ¡ 3x+4. † 15. Find all points of the curve y = 10¡x2 such that the tangent line is horizontal (i.e., has a slope of ...
t) dt. Thus, using the rst part of the fundamental theorem of calculus, G0(x) = f(x) = cos(p x) (d) y= R x4 0 cos2( ) d Note that the rst part of the fundamental theorem of calculus only allows for the derivative with respect to the upper limit (assuming the lower is constant). In this case, however, the upper limit isn't just x, but rather ...
Homework from Chapter 2, continued Lesson 4 Quiz over Lessons 1-3 (2.3): From the text, 1-16, 19-24, 26- 30 , 35-38, 41, 42 Continuity; (how does this involve the Intermediate Value Theorem?) removable discontinuities (A) A very important function in electrical engineering is the so-called "sinc" function, defined by setting ...
Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using our accompanying online resources.
The Calculus Worksheets are randomly created and will never repeat so you have an endless supply of quality Calculus Worksheets to use in the classroom or at home. These Calculus Worksheets consist of Integration, Differential Equation, Differentiation, and applications Worksheets for your use. Our Calculus Worksheets are free to download, easy ...
14. Let Rbe the region enclosed by y= x, y= 8x, and y= 4. (a) Compute the area of Rby evaluating an integral (or integrals) in terms of x. (b) Compute the area of Rby evaluating an integral (or integrals) in terms of y.
already is a version of the fundamental theorem of calculus. It will lead to the in-tegral R x 0 f(x) dx , derivative d dx f(x) and the fundamental theorem of calculus R x 0 d dt f(t )dt = x(0); d dx R x 0 1.11. This is a fantastic result. The goal of this course is to understand this theorem, and to apply it. Note that if we de ne [n]0 = 1;[n ...
Advanced Calculus: Homework 7 Problems from the textbook: Page 320, Exercises 2.1, 2.2, 2.3, 2.9
INTRODUCTION TO CALCULUS MATH 1A Unit 4: Continuity Lecture 4.1. Continuity is one of the most important concepts in mathematics: De nition: A function fis continuous at a point x 0 if a value f(x 0) can be found such that f(x) !f(x 0) for x!x 0. A function fis con-tinuous on [a;b] if it is continuous for every point xin the interval [a;b]. 4.2.
First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike.It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.. The complete textbook (PDF) is also available as a single file.
This booklet contains worksheets for the Math 180 Calculus 1 course at the University of Illinois at Chicago. There are 27 worksheets, each covering a certain topic of the course curriculum. At the end of the booklet there are 2 review worksheets, covering parts of the course (based on a two-midterm model). In a 15-week semester, completing 2 ...
The dot product gives an easy way of computing the angle between two vectors: the relationship is given by the formula a b = |a||b| cos θ. In particular, a and b are perpendicular if and only if a b = 0. Another way of multiplying vectors in R3 is the cross product. If a = a1i + a2j + a3k and.
pdf doc ; Calculator Checklist - A list of calculator skills that are required for Calculus. pdf doc ; Pixels and the calculator screen - An exercise to illustrate the sensitivity of the window settings. pdf doc ; Homework Sample - A few examples to illustrate how homework should be written. pdf doc ; CHAPTER 1 - A Library of Functions
Calculus III (2934, Fall 2019) Worksheets Kimball Martin October 15, 2019 1. Worksheet 1: R2 and R3 1.What does R2 mean? Can you give a precise de nition? What about R3? Rn? 2.What is the right-hand rule (la regolla della mano destra)? 3.Graph x= yin R2. 4.Graph x= yin R3. 5.Graph x2 + y2 = 1 in R3.
All homework will be due at midnight (actually 11:59) on the day listed. Online Hw # 1 - Due Wednesday 1/29 Volume by Slicing (cross-section, disk, and washer) and Volume by Shells. Online Hw # 2 - Due Wednesday 2/5 Arc Length, Surface Area of Revolution, and Center of Mass. Online Hw # 3 - Due Wednesday 2/12 Integration by Parts.
In Calculus II, we built upon this idea that we can use integrals to calculate and model complex situations by accumulating the sums of simpler parts. We also learned techniques used in calculat-ing and approximating these integrals and discuss ways of modeling functions and in nite systems.
Study conceptual physics online free by downloading OpenStax's University Physics Volume 1 textbook and using our accompanying online resources.