Differential Calculus Notes For Mathematics 100 and 180

Differential Calculus Notes For Mathematics 100 and 180

Differential Calculus Notes For Mathematics 100 and 180

The contents include: The basics, Limits, Derivatives, Applications
of derivatives, Numbers, Sets, Other important sets, Functions, Parsing
formulas, Inverse functions, Another limit and computing velocity, The limit of
a function, Calculating limits with limit laws, Continuity, Revisiting tangent
lines, Interpretations of the derivative, Proofs of the arithmetic of
derivatives, Derivatives of Exponential Functions, Derivatives of trigonometric
functions, The natural logarithm, Implicit Differentiation, Inverse
Trigonometric Functions, The Mean Value Theorem, Higher order derivatives,
Velocity and acceleration, Related rates, Optimisation, Sketching graphs,
Introduction to antiderivatives, Carbon dating, Population growth, Some
examples, Further examples, The error in the Taylor polynomial approximations,
Local and global maxima and minima, Finding global maxima and minima,
Symmetries, A checklist for sketching, Sketching examples, Standard examples,
Variations.

This note explains the following topics:
Differentiation from first principles, Differentiating powers of x,
Differentiating sines and cosines, Differentiating logs and exponentials, Using
a table of derivatives, The quotient rule, The product rule, The chain rule,
Parametric differentiation, Differentiation by taking logarithms, Implicit
differentiation, Extending the table of derivatives, Tangents and normals,
Maxima and minima.

This note covers the following topics: Limits and
Continuity, Differentiation Rules, Applications of Differentiation, Curve
Sketching, Mean Value Theorem, Antiderivatives and Differential Equations,
Parametric Equations and Polar Coordinates, True Or False and Multiple Choice
Problems.

Author(s): Veselin Jungic,
Petra Menz, and Randall Pyke

This book is intended for beginners. Topics covered includes: Fundamental
Rules for Differentiation, Tangents and Normals, Asymptotes, Curvature,
Envelopes, Curve Tracing, Properties of Special Curves, Successive
Differentiation, Rolle's Theorem and Taylor's Theorem, Maxima and Minima,
Indeterminate Forms.