Differential Calculus

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Work in progress: These course notes are actively being written and may contain errors or omissions. If you spot a mistake, please let me know by email.

Course Code: MAT1CJ101  ·  Semester: I  ·  Credits: 4
Institution: Ambedkar College, University of Calicut (CUFYUGP 2024)
Textbook: Thomas & Finney — Calculus and Analytic Geometry

Complete lecture notes with worked examples, step-by-step proofs, and practice problems.

Module 0 — Precalculus

• Module 0 — Precalculus

  A refresher on sets, functions, real numbers, polynomials, exponentials/logs, and trigonometry — read before or alongside Module I. Prerequisite · not examined.

Modules

• Module I — Functions and Limits

  Functions, domain and range, composition, limits, limit laws, one-sided limits, continuity at a point

• Module II — Continuity and Differentiation

  Continuity on intervals, IVT, derivative as a limit, differentiation rules, chain rule, implicit differentiation

• Module III — Extreme Values and Mean Value Theorem

  Local and absolute extrema, critical points, Rolle's theorem, MVT, increasing/decreasing functions

• Module IV — Graphing and Asymptotes

  Concavity, inflection points, second derivative test, horizontal and vertical asymptotes, curve sketching

• Module V — Trigonometry, Optimization, and Linearization

  Derivatives of trig functions, applied optimization, linearization and differentials, Newton's method

Exam Practice

• Class Tests

  Coming soon

• Previous Year Questions

  Coming soon