Author(s): Joel Feldman, Andrew Rechnitzer and Elyse Yeager
Series: CLP Calculus 02
Edition: Exercises
Publisher: University of British Columbia
Year: 2021
Language: English
Tags: mathematics; maths; math; calc; calculus; single variable; limits; differentiation; differential; integration; integral; continuity; differentiability; analysis; real; complex; multiple variables; multivariable; multivariate; several variables; many variables
How to use this book
I The questions
Integration
Definition of the Integral
Basic properties of the definite integral
The Fundamental Theorem of Calculus
Substitution
Area between curves
Volumes
Integration by parts
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions
Numerical Integration
Improper Integrals
More Integration Examples
Applications of Integration
Work
Averages
Centre of Mass and Torque
Separable Differential Equations
Sequences and Series
Sequences
Series
Convergence Tests
Absolute and Conditional Convergence
Power Series
Taylor Series
II Hints to problems
1.1 Definition of the Integral
1.2 Basic properties of the definite integral
1.3 The Fundamental Theorem of Calculus
1.4 Substitution
1.5 Area between curves
1.6 Volumes
1.7 Integration by parts
1.8 Trigonometric Integrals
1.9 Trigonometric Substitution
1.10 Partial Fractions
1.11 Numerical Integration
1.12 Improper Integrals
1.13 More Integration Examples
2.1 Work
2.2 Averages
2.3 Centre of Mass and Torque
2.4 Separable Differential Equations
3.1 Sequences
3.2 Series
3.3 Convergence Tests
3.4 Absolute and Conditional Convergence
3.5 Power Series
3.6 Taylor Series
III Answers to problems
1.1 Definition of the Integral
1.2 Basic properties of the definite integral
1.3 The Fundamental Theorem of Calculus
1.4 Substitution
1.5 Area between curves
1.6 Volumes
1.7 Integration by parts
1.8 Trigonometric Integrals
1.9 Trigonometric Substitution
1.10 Partial Fractions
1.11 Numerical Integration
1.12 Improper Integrals
1.13 More Integration Examples
2.1 Work
2.2 Averages
2.3 Centre of Mass and Torque
2.4 Separable Differential Equations
3.1 Sequences
3.2 Series
3.3 Convergence Tests
3.4 Absolute and Conditional Convergence
3.5 Power Series
3.6 Taylor Series
IV Solutions to problems
1.1 Definition of the Integral
1.2 Basic properties of the definite integral
1.3 The Fundamental Theorem of Calculus
1.4 Substitution
1.5 Area between curves
1.6 Volumes
1.7 Integration by parts
1.8 Trigonometric Integrals
1.9 Trigonometric Substitution
1.10 Partial Fractions
1.11 Numerical Integration
1.12 Improper Integrals
1.13 More Integration Examples
2.1 Work
2.2 Averages
2.3 Centre of Mass and Torque
2.4 Separable Differential Equations
3.1 Sequences
3.2 Series
3.3 Convergence Tests
3.4 Absolute and Conditional Convergence
3.5 Power Series
3.6 Taylor Series
