 COURSE SUMMARY
Course Title:
Calculus and Matrix Algebra
Course Code:
15MAT111
Year Taught:
2015
2016
2017
2018
Semester:
1
Type:
Foundation Core
Degree:
School:
School of Engineering
Campus:
Bengaluru
Chennai
Coimbatore
Amritapuri

'Calculus and Matrix Algebra' is a course offered in the first semester of B. Tech. programs at School of Engineering, Amrita Vishwa Vidyapeetham.

#### 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.

#### TEXTBOOKS / REFERENCES

TEXTBOOKS

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

REFERENCE BOOKS

• ‘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.