Book Summary of Problems in Calculus of One Variable
Table of Contents
Introduction: Problems in Calculus of One Variable
Introduction: Problems in Calculus of One Variable
1. Introduction of Mathematical Analysis
1. Real Numbers. The Absolute Value of Real Number
2. Function. Domain of Definition
3. Investigation of Functions
4. Inverse Function
5. Graphical Representation of Function
6. Number Sequences. Limit of a Sequence
7. Evaluation of a Limits of Sequences
8. Testing Sequences for Convergence
9. The Limit of a Function
10. Calculation of Limits of Functions
11. Infinitesimal and Infinite Functions. Their Definitions and Comparison
12. Equivalent Infinitesimals. Application of Finding Limits
13. One-Sides Limits
14. Continuity of a Composite Function. Points of Discontinuity and Their Classification
15. Arithmetical Operations on Continuous Functions. Continuity of a Composite Function
16. The Properties of a Function. Continuous on a Closed Interval. Continuity of an Inverse Function
17. Additional Problems
2. Function. Domain of Definition
3. Investigation of Functions
4. Inverse Function
5. Graphical Representation of Function
6. Number Sequences. Limit of a Sequence
7. Evaluation of a Limits of Sequences
8. Testing Sequences for Convergence
9. The Limit of a Function
10. Calculation of Limits of Functions
11. Infinitesimal and Infinite Functions. Their Definitions and Comparison
12. Equivalent Infinitesimals. Application of Finding Limits
13. One-Sides Limits
14. Continuity of a Composite Function. Points of Discontinuity and Their Classification
15. Arithmetical Operations on Continuous Functions. Continuity of a Composite Function
16. The Properties of a Function. Continuous on a Closed Interval. Continuity of an Inverse Function
17. Additional Problems
2. Differentiation of Functions
1. Definition of the Derivative
2. Differentiation of Explicit Functions
3. Successive Differentiation of Explicit Functions. Leibnitz Formula
4. Differentiation of Inverse, Implicit and Parametrically Represented Functions
5. Application of the Derivative
6. The Differential of a Function. Application to Approximate Computations
7. Additional Problems
3. Application of Differential Calculus to Investigation of Functions
1. Basic Theorems on Differentiable Functions
2. Evaluation of Indeterminate Forms. L ‘Hospital’s Rule
3. Taylor’s Formula. Application to Approximate Calculations
4. Application of Taylor’s Formula to Evaluation of Limits
5. Testing a Function of Monotonicity
6. Maxima and Minima of a Function
7. Finding the Greatest and Least values of a Function
8. Solving Problems in Geometry and Physics
9. Convexity and Concavity of a Curve. Points of Inflection
10. Asymptotes
11. General Plan for Investigating Function and Sketching Graphs
12. Approximate Solutions of Algebraic and Transcendental Equations
2. Evaluation of Indeterminate Forms. L ‘Hospital’s Rule
3. Taylor’s Formula. Application to Approximate Calculations
4. Application of Taylor’s Formula to Evaluation of Limits
5. Testing a Function of Monotonicity
6. Maxima and Minima of a Function
7. Finding the Greatest and Least values of a Function
8. Solving Problems in Geometry and Physics
9. Convexity and Concavity of a Curve. Points of Inflection
10. Asymptotes
11. General Plan for Investigating Function and Sketching Graphs
12. Approximate Solutions of Algebraic and Transcendental Equations
4. Indefinite Integrals. Basic Methods of Integration
1. Direct Integration and the Methods of Expansions
2. Integration by Substitution
3. Integration by Parts
4. Reduction Formula
2. Integration by Substitution
3. Integration by Parts
4. Reduction Formula
5. Basic Classes of Integral Functions
1. Integration of Rational Functions
2. Integration of Certain Irrational Expressions
3. Euler’s Substitutions
4. Other Methods of Integration Irrational Expressions
5. Integration of Binomial Differential
6. Integration of Trigonometric and Hyperbolic Functions
7. Integration of Certain Irrational Function with the Aid of Trigonometric or Hyperbolic Substitutions
8. Integration of Other Transcendental Functions
9. Methods of Integration (List of Basic Forms of Integrals)
2. Integration of Certain Irrational Expressions
3. Euler’s Substitutions
4. Other Methods of Integration Irrational Expressions
5. Integration of Binomial Differential
6. Integration of Trigonometric and Hyperbolic Functions
7. Integration of Certain Irrational Function with the Aid of Trigonometric or Hyperbolic Substitutions
8. Integration of Other Transcendental Functions
9. Methods of Integration (List of Basic Forms of Integrals)
6. The Definite Integral
1. Statement of the Problem. The Lower and Upper Integral Sums.
2. Evaluating Definite by the Newton-Leibnitz Formula
3. Estimating an Integral. The Definite Integral as a Function of its Limits
4. Changing the Variable in a Definite Integral
5. Simplification of Integrals Based on the Properties of Symmetry of Integrals.
6. Integration by Parts. Reduction Formulas.
7. Approximating Definite Integrals
8. Additional Problems
2. Evaluating Definite by the Newton-Leibnitz Formula
3. Estimating an Integral. The Definite Integral as a Function of its Limits
4. Changing the Variable in a Definite Integral
5. Simplification of Integrals Based on the Properties of Symmetry of Integrals.
6. Integration by Parts. Reduction Formulas.
7. Approximating Definite Integrals
8. Additional Problems
7. Application of the Definite Integral
1. Computing the Limits of Sums with the Aid of Definite Integrals
2. Finding average Values of a Function
3. Computing Areas in Rectangular Coordinates
4. Computing Areas with Parametrically Represented Boundaries
5. The Area of Curvilinear Sector in Polar Coordinates
6. Computing the Volume of Solid
7. The Arc Length of a Plane Curve in Rectangular Coordinates
8. The Arc Length of a Curve Represented Parametrically
9. The Arc Length of Curve in polar Coordinates
10. Area of Surface of Revolution
11. Geometrical Applications if the Definite Integral
12. Computing Pressure, Work and Other Physical Quantities by the Definite Integral
13. Computing Static Moments and Moments of Inertia. Determining Coordinates of the Centre of Gravity
14. Additional Problems
2. Finding average Values of a Function
3. Computing Areas in Rectangular Coordinates
4. Computing Areas with Parametrically Represented Boundaries
5. The Area of Curvilinear Sector in Polar Coordinates
6. Computing the Volume of Solid
7. The Arc Length of a Plane Curve in Rectangular Coordinates
8. The Arc Length of a Curve Represented Parametrically
9. The Arc Length of Curve in polar Coordinates
10. Area of Surface of Revolution
11. Geometrical Applications if the Definite Integral
12. Computing Pressure, Work and Other Physical Quantities by the Definite Integral
13. Computing Static Moments and Moments of Inertia. Determining Coordinates of the Centre of Gravity
14. Additional Problems
8. Improper Integrals
1. Improper Integrals with Infinite Limits
2. Improper Integrals of Unbounded Functions
3. Geometric and Physical Applications of Improper Integrals
4. Additional Problems
Answer and Hints
2. Improper Integrals of Unbounded Functions
3. Geometric and Physical Applications of Improper Integrals
4. Additional Problems
Answer and Hints
Details of Book: Problems in Calculus of One Variable
| Book: | Problems in Calculus of One Variable |
| Author: | IA Maron |
| ISBN: | 8183486215 |
| ISBN-13: | 9788183486217,978-8183486217 |
| Binding: | Paperback |
| Publishing Date: | 2012 |
| Publisher: | Arihant Publications |
| Edition: | 1stEdition |
| Number of Pages: | 424 |
| Language: | English |
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