RES.18-001 | Fall 2023 | Undergraduate

Calculus Online Textbook

Instructor's Manual

Instructor’s Manual Components

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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (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 Manual (PDF)
16: Mathematics after Calculus           Chapter 16 Manual (PDF)

Course Info

Departments
As Taught In
Fall 2023
Learning Resource Types
Online Textbook