Study Guide | Calculus Online Textbook

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 1.7 Computing in Calculus	(PDF - 1.2MB)
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	(PDF - 1.1MB)
3: Applications of the Derivative 3.1 Linear Approximation 3.2 Maximum and Minimum Problems 3.3 Second Derivatives: Minimum vs. Maximum 3.4 Graphs 3.5 Ellipses, Parabolas, and Hyperbolas 3.6 Iterations x,+ ,= F(x,) 3.7 Newton's Method and Chaos 3.8 The Mean Value Theorem and l'Hôpital's Rule	(PDF - 1.5MB)
4: The Chain Rule 4.1 Derivatives by the Charin Rule 4.2 Implicit Differentiation and Related Rates 4.3 Inverse Functions and Their Derivatives 4.4 Inverses of Trigonometric Functions	(PDF)
5: Integrals 5.1 The Idea of an Integral 5.2 Antiderivatives 5.3 Summation vs. Integration 5.4 Indefinite Integrals and Substitutions 5.5 The Definite Integral 5.6 Properties of the Integral and the Average Value 5.7 The Fundamental Theorem and Its Consequences 5.8 Numerical Integration	(PDF - 1.3MB)
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	(PDF - 1.5MB)
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	(PDF - 1.1MB)
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	(PDF - 1.2MB)
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	(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	(PDF - 1.3MB)
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 in Three Dimensions	(PDF)
12: Motion along a Curve 12.1 The Position Vector 12.2 Plane Motion: Projectiles and Cycloids 12.3 Tangent Vector and Normal Vector 12.4 Polar Coordinates and Planetary Motion	(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	(PDF - 1.3MB)
14: Multiple Integrals 14.1 Double Integrals 14.2 Changing to Better Coordinates 14.3 Triple Integrals 14.4 Cylindrical and Spherical Coordinates	(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	(PDF - 1.3MB)