**Book Detail:** Engineering Mathematics-I

Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry.

**Language:** English

**Pages:** 368

**Author:** Prof. C. Nahak, Prof. J. Kumar & Prof. S. Kumar

** Price:** Free

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## Outlines of Engineering Mathematics-I

### Module 1: Differential Calculus

Lesson 1: Rolle’s Theorem, Lagrange’s Mean Value Theorem, Cauchy’s Mean Value Theorem

Lesson 2: Taylor’s Theorem / Taylor’s Expansion, Maclaurin’s Expansion

Lesson 3: Indeterminate forms ; L’Hospital’s Rule

Lesson 4: Limit, Continuity of Functions of Two Variables

Lesson 5: Partial and Total Derivatives

Lesson 6: Homogeneous Functions, Euler’s Theorem

Lesson 7: Composite and Implicit functions for Two Variables

Lesson 8: Derivative of Higher Order

Lesson 9: Taylor’s Expansion for Function of Two Variables

Lesson 10: Maximum and Minimum of Function of Two Variables

Lesson 11: Lagrange’s Multiplier Rule / Constrained Optimization

Lesson 12: Convexity, Concavity and Points of Inflexion

Lesson 13: Curvature

Lesson 14: Asymptotes

Lesson 15: Tracing of Curves

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### Module 2: Integral Calculus

Lesson16: Improper Integral

Lesson17. Test for Convergence

Lesson 18: Rectification

Lesson 19: Volume and Surface of Revolution

Lesson 20: Double Integration

Lesson 21: Triple Integration

Lesson 22: Area & Volume using Double and Triple Integration

Lesson 23: Gamma Function

Lesson 24: The Beta Function

### Module 3: Ordinary Differential Equations

Lesson 25: Introduction

Lesson 26: Differential Equations of First Order

Lesson 27: Linear Differential Equation of First Order

Lesson 28: Exact Differential Equations of First Order

Lesson 29: Exact Differential Equations : Integrating Factors

Lesson 30: Linear Differential Equations of Higher Order

Lesson 31: Linear Differential Equations of Higher Order

Lesson 32: Linear Differential Equations of Higher Order (Cont.)

Lesson 33: Method of Undetermined Coefficients

Lesson 34: Method of Variation of Parameters

Lesson 35: Equations Reducible to Linear Differential Equations with Constant Coefficient

Lesson 36: Methods for Solving Simultaneoous Ordinary Differential Equations

Lesson 37: Series Solutions about an Ordinary Point

Lesson 38: Series Solutions about an Ordinary Points (Cont.)

Lesson 39: Series Solutions about a Regular Singular Point

Lesson 40: Series Solutions about a Regular Singular Point (Cont..)

### Module 4: Vector Calculus

Lesson 41: Introduction

Lesson 42: Gradient and Directional Derivatives

Lesson 43: Divergence and Curl

Lesson 44: Line Integral

Lesson 45: Green’s Theorem in the Plane

Lesson 46: Surface Integral

Lesson 47: Stokes’s Theorem

Lesson 48: Divergence Theorem of Gauss

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