Author(s): Fabio Cirrito et. al.
Publisher: IBID Press
Year: 2006
Language: English
Pages: 182
Contents
1.1 Sequences
1.1.1 Introduction
Exercises 1.1.1
Answers 1.1.1
1.1.2 Visualising Sequences - Graphs
Exercises 1.1.2
Answers 1.1.2
1.2 Limits of Sequences
1.2.1 Introduction
Exercises 1.2.1
Answers 1.2.1
1.2.2 Defining the limit of a sequence
Exercises 1.2.2
Answers 1.2.2
1.2.3 More Limit Definitions
Squeeze Theorem
Exercises 1.2.3
Answers 1.2.3
1.2.4 Algebra of Limits
Exercises 1.2.4
Answers 1.2.4
Exercises 1.2.5 - Miscellanoeus
Answers 1.2.5
1.3 Limit of a Function
1.3.1 Sequences as Functions
1.3.2 l'Hospital's Rule
Exercises 1.3
Answers 1.3
1.4 Improper Integrals
1.4.1 What are Improper Integrals
1.4.2 Evaluating Improper Integrals
1.4.3 Comparison test for improper integrals
Exercises 1.4
Answers 1.4
2.1 Series
2.1.1 Introduction
2.1.2 Sum of a Series
2.1.3 Criteria for Convergence
2.1.4 Necessary Condition for convergence
2.1.5 The number e
2.1.6 Sufficient condition for convergence
Limit Comparison Test
Ratio Test (D'Alembert's Criterion)
Telescoping Series
Partial Fractions
Integral Test
Exercises 2.1
Answers 2.1
2.2 More use of integrals
2.2.1 Comparing series & integrals
2.2.2 Errors in approximating infinite series
Exercises 2.2
Answers 2.2
2.3 Summary: Which test to use
3.1 Alternating Series
3.1.1 Introduction
Exercises 3.1
Answers 3.1
3.2 Other Types of Convergence
3.2.1 Conditional and Absolute Convergence
Exercises 3.2
Answers 3.2
3.3 Power Series
3.3.1 Power series & Radius of convergence
3.3.2 Convergence Interval of a Power Series
3.3.3 Radius or interval?
3.3.4 Power series in (x-k)
Exercises 3.3
Answers 3.3
3.4 Calculus with Power Series
3.4.1 Power Series as functions
3.4.2 Differentiating and integrating power series
3.4.3 Using power series to solve integrals
Exercises 3.4
Answers 3.4
4.1 Series Expansion
4.1.1 Introduction - Polynomials
4.1.2 Coefficients of polynomials in terms of derivatives
4.1.3 Approximating function by a polynomial
1. Near x = 0
2. Near x = a
4.1.4 Taylor and Maclaurin Series
1. Accuracy & Maclaurin series
2. Examples: sinx & (1+x)^n
4.1.5 Trig functions
4.1.6 More Maclaurin expansions
1. Exponential functions
2. Logarithmic functions
3. Inverse trig relations
4.1.7 Taylor series
4.1.8 Summary of Maclaurin & Taylor
Exercises 4.1
Answers 4.1
4.2 Series expansions of Combined Expressions
4.2.1 Expansion of Composite Functions
4.2.2 Taylor expansions involving multiplication
Exercises 4.2
Answers 4.2
4.3 More Applications
4.3.1 Two definite integrals
Exercises 4.3
Answers 4.3
5.1 Differential Equations
5.1.1 Definitions
Exercises 5.1
Answers 5.1 (solution manual)
5.2 Geometrical Method
5.2.1 Slope Fields
Exercises 5.2
Answers 5.2 (solution manual)
5.3 Numerical Method
5.3.1 Euler's method
Exercises 5.3
Answers 5.3
5.4 Two First order DEs
5.4.1 Homogeneous firsdt order DE
Exercises 5.4.1
Answers 5.4.1
5.4.2 The Integrating factor
Exercises 5.4.2
Answers 5.4.2 (NA)
