Syllabus
Unit 1
Review Functions, shifting, and scaling. Limits, one-sided limits, and limits at infinity, Continuity, types of discontinuities.
Unit 2
Derivatives, differentiation techniques, implicit differentiation. Applications of Derivative Extreme values of functions, Concavity, and Curve Sketching.
Unit 3
Integration – Definite Integrals, Properties of definite integrals. Integration techniques integration by parts and integration by substitution. Fundamental theorem of Calculus. Applications of Integrals -Volumes by slicing and rotation about an axis.
Unit 4
Review Matrices, operations on matrices, determinants. Linear systems, Gauss elimination, linear independence, rank of a matrix.
Unit 5
Eigenvalues and eigenvectors, Symmetric, Skew Symmetric and Orthogonal matrices, Eigen bases, Diagonalization.
Objectives and Outcomes
Course Outcomes:
CO1: Understand the elementary functions and concepts of limit, continuity, derivative, and integral
CO2: Analyze various techniques of differentiation and integration.
CO3: Applications of differentiation and integration.
CO4: Evaluate linear independence and rank and solve for a system of linear equations.
CO5: Analyze the notion of eigenvalues and eigenvectors, eigen basis and the possibility ofdiagonalization
Text Books / References
TEXTBOOKS:
1. Calculus, G. B. Thomas, Pearson, 2009, Eleventh Edition.
2. Advanced Engineering Mathematics, Erwin Kreyszig, Wiley India, Tenth Edition, 2015.
REFERENCE BOOKS :
1. George Turrell, Mathematics for Chemistry and Physics, Academic Press, 2002.
2. Herbert S. Wilf, Applied Mathematics for Physical Chemistry, 2nd Edition, Prentice Hall, 1998.
