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 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.
These notes are
intended as a brief introduction to some of the main ideas and
methods of calculus. Topics covered includes: Functions and Graphs,
Linear Functions, Lines, and Linear Equations, Limits, Continuity,
Linear Approximation, Introduction to the Derivative, Product,
Quotient, and Chain Rules, Derivatives and Rates, Increasing and
Decreasing Functions, Concavity, Optimization, Exponential and
Logarithmic Functions, Antiderivatives, Integrals.
This note
explains following topics: Ordinary Differential Equations, First-Order
Differential Equations, Second Order Differential Equations, Third and
Higher-Order Linear ODEs, Sets of Linear, First-Order, Constant-Coefficient
ODEs,Power-Series Solution, Vector Analysis, Complex Analysis, Complex Analysis,
Complex Functions.
This book covers the following
topics: Analytic Geometry, Instantaneous Rate Of Change: The Derivative, Rules
For Finding Derivatives, Transcendental Functions, Curve Sketching, Applications
of the Derivative, Integration, Techniques of Integration, Applications of
Integration, Sequences and Series.
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.
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.
This note explains the following topics:
Functions and Their Graphs, Trigonometric Functions, Exponential Functions,
Limits and Continuity, Differentiation, Differentiation Rules, Implicit
Differentiation, Inverse Trigonometric Functions, Derivatives of Inverse
Functions and Logarithms, Applications of Derivatives, Extreme Values of
Functions, The Mean Value Theorem, Monotone Functions and the First Derivative
Test, Integration, Sigma Notation and Limits of Finite Sums, Indefinite
Integrals and the Substitution Method.
This note
explains the following topics: Calculus is probably not the most popular course
for computer scientists. Calculus – FAQ, Real and complex numbers, Functions,
Sequences, Series, Limit of a function at a point, Continuous functions, The
derivative, Integrals, Definite integral, Applications of integrals, Improper
integrals, Wallis’ and Stirling’s formulas, Numerical integration, Function
sequences and series.
This note covers the following
topics: Numbers and Functions, Derivatives, Limits and Continuous Functions,
Graph Sketching and Max-Min Problems, Exponentials and Logarithms, The Integral,
Applications of the integral.
These
notes are not intended as a textbook. It is hoped however that they will
minimize the amount of note taking activity which occupies so much of a
student’s class time in most courses in mathmatics. Topics covered includes: The
Real Number system & Finite Dimensional Cartesian Space, Limits, Continuity, and
Differentiation, Riemann Integration, Differentiation of Functions of Several
Variables.
The approach followed is quite
different from that of standard calculus texts. We use natural, but occasionally
unusual, definitions for basic concepts such as limits and tangents. Topics
covered includes: Sets: Language and Notation, The Extended Real Line, Suprema,
Infima, Completeness, Neighborhoods, Open Sets and Closed Sets, Trigonometric
Functions, Continuity, The Intermediate Value Theorem, Inverse Functions,
Tangents, Slopes and Derivatives, Derivatives of Trigonometric Functions, Using
Derivatives for Extrema, Convexity, Integration Techniques.
This notes contains the details about The untyped lambda calculus, The
Church-Rosser Theorem, Combinatory algebras, The Curry-Howard isomorphism,
Polymorphism, Weak and strong normalization, Denotational semantics of PCF
This notes contain Complex numbers, Proof by induction, Trigonometric and
hyperbolic functions, Functions, limits, differentiation, Integration, Taylor’s
theorem and series
This book emphasizes the fundamental concepts from calculus and
analytic geometry and the application of these concepts to selected areas of
science and engineering. Topics covered includes: Sets,
Functions, Graphs and Limits, Differential Calculus, Integral Calculus,
Sequences, Summations and Products and Applications of Calculus.