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
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: 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, 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.
The note
is intended as a one and a half term course in calculus for students who have
studied calculus in high school. It is intended to be self contained, so that it
is possible to follow it without any background in calculus, for the
adventurous.
This note covers following topics of Integral and
Differential Calculus: Differential Calculus: rates of change, speed, slope of a graph, minimum
and maximum of functions, Derivatives measure instantaneous changes, Integral
Calculus: Integrals measure the accumulation of some quantity, the total
distance an object has travelled, area under a curve, volume of a region.
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.
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.
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
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.