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**Author:**Richard Courant**Title:**Differential and Integral Calculus**Amazon Link:**

https://www.amazon.com/dp/4871878384/?tag=pfamazon01-20

https://www.amazon.com/dp/487187835X/?tag=pfamazon01-20**Prerequisities:**

**Table of Contents of Volume 1:**

Code:

```
[LIST]
[*] Introductory Remarks
[*] Introduction
[LIST]
[*] The Continuum of Numbers
[*] The Concept of function
[*] More Detailed Study of the Elementary Functions
[*] Functions of an Integral Variable. Sequences of Numbers
[*] The Concept of the Limit of a Sequence
[*] Further Discussion of the Concept of Limit
[*] The Concept of Limit where the Variable is Continuous
[*] The Concept of Continuity
[/LIST]
[*] Appendix
[LIST]
[*] Preliminary Remarks
[*] The Principle of the Point of Accumulation and its Applications
[*] Theorems on Continuous Functions
[*] Some Remarks on the Elementary Functions
[/LIST]
[*] Appendix
[LIST]
[*] Polar Co-ordinates
[*] Remarks on Complex Numbers
[/LIST]
[*] The Fundamental Ideas of the Integral and Differential Calculus
[LIST]
[*] The Definite Integral
[*] Examples
[*] The Derivative
[*] The Indefinite Integral, the Primitive Function, and the Fundamental Theorems of the Differential and Integral Calculus
[*] Simple Methods of Graphical Integration
[*] Further Remarks on the Connexion between the Integral and the
Derivative
[*] The Estimation of Integrals and the Mean Value Theorem of the
Integral Calculus
[/LIST]
[*] Appendix
[LIST]
[*] The Existence of the Definite Integral of a Continuous Function
[*] The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus
[/LIST]
[*] Differentiation and Integration of The Elementary Functions
[LIST]
[*] The Simplest Rules for Differentiation and their Applications
[*] The Corresponding Integral Formulae
[*] The Inverse Function and its Derivative
[*] Differentiation of a Function of a Function
[*] Maxima and Minima
[*] The Logarithm and the Exponential Function
[*] Some Applications of the Exponential Function
[*] The Hyperbolic Functions
[*] The Order of Magnitude of Functions
[/LIST]
[*] Appendix
[LIST]
[*] Some Special Functions
[*] Remarks on the Differentiability of Functions
[*] Some Special Formulae
[/LIST]
[*] Further Development of the Integral Calculus
[LIST]
[*] Elementary Integrals
[*] The Method of Substitution
[*] Further Examples of the Substitution Methods
[*] Integration by Parts
[*] Integration of Rational Functions
[*] Integration of some Other Classes of Functions
[*] Remarks on Functions which are not Integrable in Terms of Elementary Functions
[*] Extension of the Concept Integral. Improper Integrals
[/LIST]
[*] Appendix
[LIST]
[*] The Second Mean Value Theorem of the Integral Calculus
[/LIST]
[*] Applications
[LIST]
[*] Representation of Curves
[*] Applications to the Theory of Plane Curves
[*] Examples
[*] Some Very Simple Problems in the Mechanics of a Particle
[*] Further Applications: Particle Sliding down a Curve
[*] Work
[/LIST]
[*] Appendix
[LIST]
[*] Properties of the Evolute
[*] Area bounded by Closed Curves
[/LIST]
[*] Taylor's Theorem and the Approximate Expression of Functions by Polynomials
[LIST]
[*] The Logarithm and the Inverse Tangent
[*] Taylor's Theorem
[*] Applications. Expansions of the Elementary Functions
[*] Geometrical Applications
[/LIST]
[*] Appendix
[LIST]
[*] Example of a Function which cannot be expanded in a Taylor
Series
[*] Proof that e is Irrational
[*] Proof that the Binomial Series Converges
[*] Zeros and Infinities of Functions, and So-called Indeterminate Expressions
[/LIST]
[*] Numerical Methods
[LIST]
[*] Preliminary Remarks
[*] Numerical Integration
[*] Applications of the Mean Value Theorem and of Taylor's Theorem. The Calculus of Errors
[*] Numerical Solution of Equations
[/LIST]
[*] Appendix
[LIST]
[*] Stirling's Formula
[/LIST]
[*] Infinite Series and Other Limiting Processes
[LIST]
[*] Preliminary Remarks
[*] The Concepts of Convergence and Divergence
[*] Tests for Convergence and Divergence
[*] Sequences and Series of Fnnctions
[*] Uniform and Non-uniform Convergence
[*] Power Series
[*] Expansion of Given Functions in Power Series. Method of Undetermined Coefficients. Examples
[*] Power Series with Complex Terms
[/LIST]
[*] Appendix
[LIST]
[*] Multiplication and Division of Series
[*] Infinite Series and Improper Integrals
[*] Infinite Products
[*] Series involving Bernoulli's Numbers
[/LIST]
[*] Fourier Series
[LIST]
[*] Periodic Functions
[*] Use of Complex Notation
[*] Fourier Series
[*] Examples of Fourier Series
[*] The Convergence of Fourier Series
[/LIST]
[*] Appendix
[LIST]
[*] Integration of Fourier Series
[/LIST]
[*]A Sketch of The Theory of Functions of Several Variables
[LIST]
[*] The Concept of Function in the Case of Several Variables
[*] Continuity
[*] The Derivatives of a Function of Several Variables
[*] The Chain Rule and the Differentiation of Inverse Functions
[*] Implicit Functions
[*] Multiple and Repeated Integrals
[/LIST]
[*] The Differential Equations for the Simplest Types of Vibration
[LIST]
[*] Vibration Problems of Mechanics and Physics
[*] Solution of the Homogeneous Equation. Free Oscillations
[*] The Non-homogeneous Equation. Forced Oscillations
[*] Additional Remarks on Differential Equations
[/LIST]
[*] Summary of Important Theorems and Formulas
[*] Miscellaneous Examples
[*] Answers and Hints
[*] Index
[/LIST]
```

**Table of Contents of Volume 2:**

Code:

```
[LIST]
[*] Preliminary Remarks on Analytical Geometry and Vector Analysis
[LIST]
[*] Rectangular Co-ordinates and Vectors
[*] The Area of a Triangle, the Volume of a Tetrahedron, the Vector Multiplication of Vectors
[*] Simple Theorems on Determinants of the Second and Third Order
[*] Affine Transformations and the Multiplication of Determinants
[/LIST]
[*] Functions of Several Variables and Their Derivatives
[LIST]
[*] The Concept of Function in the Case of Several Variables
[*] Continuity
[*] The Derivatives of a Function
[*] The Total Differential of a Function and its Geometrical Meaning
[*] Functions of Functions (Compound Functions) and the Introduction of New Independent Variables
[*] The Mean Value Theorem and Taylor's Theorem for Functions of Several Variables
[*] The Application of Vector Methods
[/LIST]
[*] Appendix
[LIST]
[*] The Principle of the Point of Accumulation in Several Dimensions and its Applications
[*] The Concept of Limit for Functions of Several Variables
[*] Homogeneous Functions
[/LIST]
[*] Developments and Applications of the Differential Calculus
[LIST]
[*] Implicit Functions
[*] Curves and Surfaces in Implicit Form
[*] Systems of Functions, Transformations, and Mappings
[*] Applications
[*] Families of Curves, Families of Surfaces, and their Envelopes
[*] Maxima and Minima
[/LIST]
[*] Appendix
[LIST]
[*] Sufficient Conditions for Extreme Values
[*] Singular Points of Plane Curves
[*] Singular Points of Surfaces
[*] Connexion between Euler's and Lagrange's Representations of the Motion of a Fluid
[*] Tangential Representation of a Closed Curve
[/LIST]
[*] Multiple Integrals
[LIST]
[*] Ordinary Integrals as Functions of a Parameter
[*] The Integral of a Continuous Function over a Region of the Plane or of Space
[*] Reduction of the Multiple Integral to Repeated Single Integrals
[*] Transformation of Multiple Integrals
[*] Improper Integrals
[*] Geometrical Applications
[*] Physical Applications
[/LIST]
[*] Appendix
[LIST]
[*] The Existence of the Multiple Integral
[*] General Formula for the Area (or Volume) of a Region bounded by Segments of Straight Lines or Plane Areas (Gukhn's Formula). The Polar Planimeter
[*] Volumes and Areas in Space of any Number of Dimensions
[*] Improper Integrals as Functions of a Parameter
[*] The Fourier Integral
[*] The Eulerian Integrals (Gamma Function)
[*] Differentiation and Integration to Fractional Order. Abel's Integral Equation
[*] Note on the Definition of the Area of a Curved Surface
[/LIST]
[*] Integration over Regions in Several Dimension
[LIST]
[*] Line Integrals
[*] Connexion between Line Integrals and Double Integrals in the Plane. (The Integral Theorems of Gauss, Stokes, and Green)
[*] Interpretation and Applications of the Integral Theorems for the Plane
[*] Surface Integrals
[*] Gauss's Theorem and Green's Theorem in Space
[*] Stokes's Theorem in Space
[*] The Connexion between Differentiation and Integration for Several Variables
[/LIST]
[*] Appendix
[LIST]
[*] Remarks on Gauss's Theorem and Stokes's Theorem
[*] Representation of a Source-free Vector Field as a Curl
[/LIST]
[*] Differential Equations
[LIST]
[*] The Differential Equations of the Motion of a Particle in Three Dimensions
[*] Examples on the Mechanics of a Particle
[*] Further Examples of Differential Equations
[*] Linear Differential Equations
[*] General Remarks on Differential Equations
[*] The Potential of Attracting Charges
[*] Further Examples of Partial Differential Equations
[/LIST]
[*] Calculus of Variations
[LIST]
[*] Introduction
[*] Euler's Differential Equation in the Simplest Case
[*] Generalizations
[/LIST]
[*] Functions of a Complex Variable
[LIST]
[*] Introduction
[*] Foundations of the Theory of Functions of a Complex Variable)
[*] The Integration of Analytic Functions
[*] Cauchy's Formula and its Applications
[*] Applications to Complex Integration (Contour Integration)
[*] Many-valued Functions and Analytic Extension
[/LIST]
[*] Supplement
[LIST]
[*] Real Numbers and the Concept of Limit
[*] Miscellaneous Examples
[*] Summary of Important Theorems and Formulae
[*] Answers and Hints
[*] Index
[/LIST]
[/LIST]
```

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