This note explains the following
topics: Hyperbolic Trigonometric Functions, The Fundamental Theorem of Calculus,
The Area Problem or The Definite Integral, The Anti-Derivative, Optimization,
L'Hopital's Rule, Curve Sketching, First and Second Derivative Tests, The Mean
Value Theorem, Extreme Values of a Function, Linearization and Differentials,
Inverse Trigonometric Functions, Implicit Differentiation, The Chain Rule, The
Derivative of Trig. Functions, The Differentiation Rules, Limits Involving
Infinity, Asymptotes, Continuity, Limit of a function and Limit Laws, Rates of
Change and Tangents to Curves.
This book contains below topics, Analytic Geometry, Distance Between Two Points Circles, Shifts and Dilations, Instantaneous Rate of Change The Derivative, The slope of a function, An example, The Derivative Function, Properties of Functions, Rules for Finding Derivatives, The Power Rule, Linearity of the Derivative, The Product Rule, The Quotient Rule, The Chain Rule, Transcendental Functions, Trigonometric Functions.
This note contains below topics, Matrices and linear transformations, Spaces of matrices, Some geometric situations, Immersions submersions and connections, Metric spaces.
This note covers Numbers and
Functions, Derivatives 1, Limits and Continuous Function, Derivatives 2, Graph
Sketching and Max Min Problems, Exponentials and Logarithms, The Integral and
Applications of the integral.
This is a set of
exercises and problems for a standard beginning calculus. A fair
number of the exercises involve only routine computations, many of
the exercises and most of the problems are meant to illuminate
points that in my experience students have found confusing.
This
note covers following topics, Continuity and Limits, Continuous Function, Derivatives, Derivative as a
function, Differentiation rules, Derivatives of elementary functions,
Trigonometric functions, Implicit differentiation, Inverse Functions,
Logarithmic functions and differentiation, Monotonicity, Area between two
curves.
This note
explains following topics, Ordinary Differential Equations, FirstOrder
Differential Equations, Second Order Differential Equations, Third and
HigherOrder Linear ODEs, Sets of Linear, FirstOrder, ConstantCoefficient
ODEs,PowerSeries Solution, Vector Analysis, Complex Analysis, Complex Analysis,
Complex Functions.
In this book, much emphasis is put on explanations of concepts and solutions to examples. Topics covered includes, Sets, Real Numbers and Inequalities, Functions and Graphs, Limits, Differentiation, Applications of Differentiation, Integration, Trigonometric Functions, Exponential and Logarithmic Functions.