MAT 101 - Calculus I

Syllabus for MAT 101 – Calculus I

This is a compulsory course for B.Tech. students in their 1^st semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: Class XII mathematics or MAT 100 (Precalculus)

Brief Description:

This course covers one variable calculus and applications. It forms the base for subsequent courses in advanced vector calculus and real analysis as well as for applications in probability, differential equations, optimization, etc.

Detailed Syllabus:

1. Differentiation: Functions, limits, sandwich theorem, continuity, intermediate value theorem, tangent line, rates of change, derivative as function, algebra of derivatives, implicit differentiation, related rates, linear approximation, differentiation of inverse functions, derivatives of standard functions (polynomials, rational functions, trigonometric and inverse trigonometric functions, hyperbolic and inverse hyperbolic functions).
2. Applications of Differentiation: Indeterminate forms and L'Hopital's rule, absolute and local extrema, first derivative test, Rolle's theorem, mean value theorem, concavity, 2^nd derivative test, curve sketching.
3. Integration: Area under a curve, Riemann sums, integrability, fundamental theorem, mean value theorem for integrals, substitution, integration by parts, trigonometric integrals, partial fractions, improper integrals.
4. Applications of Integration: Area between curves, volume, arc length, applications to physics (work, center of mass).
5. Ordinary Differential Equations: 1^st order and separable, logistic growth, 1^st order and linear, 2^nd order linear with constant coefficients, method of undetermined coefficients, method of variation of parameters.

Main References:

• Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.
• Advanced Engineering Mathematics, Erwin Kreyszig, 9^th edition, Wiley India, 2011.

Supplementary References:

• Advanced Engineering Mathematics, Dennis G Zill and Warren S Wright, 4^th edition, Jones and Bartlett.
• The Calculus Lifesaver, by A Banner, Princeton, 2007.
• Calculus and Analytic Geometry by G B Thomas and R L Finney, 9^th edition, Pearson.