## Course Detail

 Course Name Calculus and Matrix Algebra Course Code 15 MAT 111 Program B. Tech. (Bachelor of Technology) in Electrical and Electronics Engineering, B. Tech. in Civil Engineering, B. Tech. (Bachelor of Technology) in Aerospace Engineering, B. Tech. (Bachelor of Technology) in Mechanical Engineering, B. Tech. (Bachelor of Technology) in Computer and Communication Engineering Semester One Year Taught 2019

### Syllabus

##### Unit 1

Calculus

Graphs: Functions and their Graphs. Shifting and Scaling of Graphs.

Limit and Continuity: Limit (One-Sided and Two-Sided) of Functions. Continuous Functions, Discontinuities, Monotonic Functions, Infinite Limits and Limit at Infinity.

##### Unit 2

Differentiation and its Applications: Derivative of a function, non differentiability, Intermediate Value Property, Mean Value Theorem, Extreme Values of Functions, Monotonic Functions, Concavity and Curve Sketching, Integration: Definite Integrals, The Mean Value Theorem for definite integrals, Fundamental Theorem of Calculus, Integration Techniques.

##### Unit 3

Matrix Algebra

Review: System of linear Equations, linear independence

Eigen values and Eigen vectors: Definitions and Properties, Positive definite, Negative Definite and Indef inite Matrices, Diagonalization and Orthogonal Diagonalization, Quadratic form, Transformation of Quadratic Form to Principal axes, Symmetric and Skew Symmetric Matrices, Hermitian and Skew Hermitian Matrices and Orthogonal MatricesIterative Methods for the Solution of Linear Systems, Power Method for Eigen Values and Eigen Vectors.

### Text Books

1. ‘Calculus’, G. B. Thomas Pearson Education, 2009, Eleventh Edition.
2. ‘Advanced Engineering Mathematics’, Erwin Kreyszig, John Wiley and Sons, 2015, Tenth Edition.

### Resources

• ‘Calculus’, Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, 3rd Edition, 2002.
• ‘Advanced Engineering Mathematics’, by Dennis G. Zill and Michael R. Cullen, second edition, CBS Publishers, 2012.

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