Instructor's Manual

Instructor’s Manual Components

  • Notes on the Text (PDF)
  • Selected Errata (PDF)

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)
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)
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 - 1.4MB)
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)
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 - 1.1MB)
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)
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 - 1.0MB)
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)
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 - 1.0MB)
16: Mathematics after Calculus
16.1 Linear Algebra          
16.2 Differential Equations          
16.3 Discrete Mathematics
(PDF)

Course Info

Learning Resource Types

menu_book Online Textbook