This book explains the
following topics: Derivatives, Derivatives, slope, velocity, rate of
change, Limits, continuity, Trigonometric limits, Derivatives of
products, quotients, sine, cosine, Chain rule, Higher derivatives,
Implicit differentiation, inverses, Exponential and log, Logarithmic
differentiation, hyperbolic functions, Applications of
Differentiation, Linear and quadratic approximations ,Curve
sketching, Max-min problems, Newton’s method and other applications,
Mean value theorem, Inequalities, Differentials, antiderivatives,
Differential equations, separation of variables, Integration,
Techniques of Integration.
Author(s): Prof. David Jerison,
Massachusetts Institute of Technology
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 book explains the
following topics: Derivatives, Derivatives, slope, velocity, rate of
change, Limits, continuity, Trigonometric limits, Derivatives of
products, quotients, sine, cosine, Chain rule, Higher derivatives,
Implicit differentiation, inverses, Exponential and log, Logarithmic
differentiation, hyperbolic functions, Applications of
Differentiation, Linear and quadratic approximations ,Curve
sketching, Max-min problems, Newton’s method and other applications,
Mean value theorem, Inequalities, Differentials, antiderivatives,
Differential equations, separation of variables, Integration,
Techniques of Integration.
Author(s): Prof. David Jerison,
Massachusetts Institute of Technology
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 emphasizes
careful reasoning and understanding of proofs. It assumes knowledge of
elementary calculus. Topics covered includes: Integers and exponents, Square
roots, and the existence of irrational numbers, The Riemann condition,
Properties of integrals, Integrability of bounded piecewise-monotonic functions,
Continuity of the square root function, Rational exponents, The fundamental
theorems of calculus, The trigonometric functions, The exponential and logarithm
functions, Integration, Taylor's formula, Fourier Series.
This note covers following
topics: The Real Numbers, Basic Geometry And Trigonometry, The Complex Numbers,
Functions Of One Variable, Derivatives, Properties And Applications Of
Derivatives, Antiderivatives And Differential Equations, The Integral, Infinite
Series, Vector Valued Functions, Limits And Derivatives, Line Integrals,
Functions Of More Than One Variable, Linear Algebra, Vector Calculus.
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.
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.
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.
This book covers
the following topics: Field of Reals and Beyond,
From Finite to Uncountable Sets, Metric Spaces and Some Basic Topology,
Sequences and Series, Functions on Metric Spaces and Continuity, Riemann
Stieltjes Integration.
This lecture note explains the
following topics: Methods of integration, Taylor polynomials, complex numbers and the complex exponential, differential equations, vector geometry and
parametrized curves.
This notes contain Complex numbers, Proof by induction, Trigonometric and
hyperbolic functions, Functions, limits, differentiation, Integration, Taylor’s
theorem and series