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.
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.
The contents include: Introduction, Proof by
induction, Complex numbers, Trigonometric and hyperbolic functions, Functions,
limits and differentiation, Integration, Taylor’s theorem and series,
Exercises.
Author(s): ACC Coolen, Department of
Mathematics, King’s College London
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 explain the solution of the following two problems: obtaining of Kepler's
laws from Newton's laws and obtaining the fourth Newton's law as a corollary of
Kepler's laws. This small book is devoted to the scholars, who are interested in
physics and mathematics.