Calculus Online Textbook

Study Guide

ChapterS	FILES
1: Introduction to Calculus                 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 1 Study Guide (PDF)
2: Derivatives                 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 2 Study Guide (PDF)
3: Applications of the Derivative                 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 3 Study Guide (PDF)
4: Derivatives by the Chain Rule                 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 4 Study Guide (PDF)
5: Integrals                 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 5 Study Guide (PDF)
6: Exponentials and Logarithms                 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 6 Study Guide (PDF)
7: Techniques of Integration                 7.1 Integration by Parts                           7.2 Trigonometric Integrals                           7.3 Trigonometric Substitutions                           7.4 Partial Fractions                           7.5 Improper Integrals	Chapter 7 Study Guide (PDF)
8: Applications of the Integral                 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 8 Study Guide (PDF)
9: Polar Coordinates and Complex Numbers                 9.1 Polar Coordinates                           9.2 Polar Equations and Graphs                           9.3 Slope, Length, and Area for Polar Curves                           9.4 Complex Numbers	Chapter 9 Study Guide (PDF)
10: Infinite Series                 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 10 Study Guide (PDF)
11: Vectors and Matrices                 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 11 Study Guide (PDF)
12: Motion along a Curve                 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 12 Study Guide (PDF)
13: Partial Derivatives                 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 13 Study Guide (PDF)
14: Multiple Integrals                 14.1 Double Integrals                           14.2 Changing to Better Coordinates                           14.3 Triple Integrals                           14.4 Cylindrical and Spherical Coordinates	Chapter 14 Study Guide (PDF)
15: Vector Calculus                 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 15 Study Guide (PDF)