# Calculus

## Mathematical Methods I Fall2013

Lecture Notes on Mathematical Methods

Other Resources

Department of Aerospace and Mechanical Engineering Universityof Notre Dame

### Calculus I Pre

Textbook:Precalculus, fifth edition, by James Stewart, Lothar Redlin and Saleem Watson

Lectures notes and video

Math

Textbook: Thomas’ Calculus: Early Transcendentals (12th edition) by Weir, Hass, Giordano

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Topic: Differentiation Rules , Summation Notation and Rules ,  Limit Definition of Definite Integral ,  An Example of Limit Definition of Definite Integral , Properties of Definite Integrals ,  Mean Value Theorem for Integrals and Fundamental Theorems of Calculus  , Average Value of a Function, Even and Odd Functions  , An Example of Arc Length  , An Example of Surface Area  , Centroid and Center of Mass of a Flat Plate  , Naturally Occurring Exponential  , Carbon Dating  , Discrete and Continuous Compounding of Interest  , Exponential Decay  , Recursion (Reduction) Formulas  , Trigonometric Integrals  , Integration Techniques  , Practice Integration Problems  , Estimating the Value of Definite Integrals Using the Trapezoidal Rule and Simpson’s Rule  , The Plausibilty of Simpson’s Rule , Comparison Tests for Improper Integrals,  Graphing Using Parametric Equations, An Example of Arc Length Using Parametric Equations .

### Lecture Notes For Most Math Classes Taughtat Lake Tahoe Community College, by Larry Green

Index of Math Terms

Basic Mathematics (Math 187)

Beginning Algebra Part I  (Math 152A)

Beginning Algebra  Part II (Math 152B)

Intermediate Algebra  (Math 154)

Survey of Mathematics  (Math 102)

Elementary Statistics  (Math 201)

College Algebra Part I  (Math 103A)

College Algebra Part II (Math 103B)

Differential Calculus for Engineering and other Hard Sciences

Differential Calculus for Business and Life Sciences

Integral Calculus for Engineering and other Hard Sciences

Third Quarter Calculus for Engineering and other Hard Sciences

Integral Calculus for Business and Life Sciences

Third Quarter Calculus for Business and Life Sciences

Vector Calculus

Linear Algebra

Differential Equations

Mathematics and Gambling

CAHSEE (California High School Exit Exam Prep)

Tutoring Methods

Textbook: Advanced Engineering Mathematics“, by Ervin Kreyszig, 9th Edition, Wiley International Edition,Complex Analysis; Linear Algebra; Numerical Methods; Probability.         Lectures Tutorial Notes and Tutorial SolutionsSolutions

Textbook: Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications -Second Edition, by Brannan and Boyce; Textbook problem solution, Homework solution , exam solution; Differential equations,  Linear differential equations , The method of separation of variables, Homogeneous differential equations. Exact differential equations ; Existence and uniqueness theory for ordinary differential equations ; Systems of linear differential equations; Solving homogeneous systems with constant coefficients , Fundamental systemsMethods

onskian determinant ; 2×2 matrices; How to solve systems of ODE , An example of a 3×3 system of linear differential equations; inhomogeneous 2×2 systems; variation of parameters formula. Variation of parameters formula ; Second order linear differential equations;  Linear oscillations in the presence of an external force; Laplace transform, Solving differential equations using the Laplace transform, Nonlinear systems of differential equations;  Hamiltonian systems;  The mathematical pendulum .

Calculus Book with Video Lecture  Preliminaries, Limits and Continuity, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, Further Applications of Integration, Conic Sections and Polar Coordinates, Infinite Sequences and Series, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integration in Vector Fields, calculus exam with solution.

Recurrent Problems, Sums,  Integer functions, Number Theory, Binomial Coefficients, Special  numbers, Classical Discrete MathematicsHOMEWORK PROBLEMS SOLUTIONS

Textbook: CONCRETE MATHEMATICS A Foundation for Computer Science, Graham, Knuth, Patashnik ,Addison- Wesley

Textbook: The Humongous book of Calculus Problems by M. Kelley.

Lecture notes       Exam answers quizzes     Homework  Online tools and Data ( Wolfram Alpha – Online Gnuplot GUI) Game: Derivatives vs. anti-derivatives ;Antiderivatives and differential equations Case Study: Tracking Mountain Lions ;Antiderivatives and differential equations ;Autonomous differential equations Case study: Bacteria Reproduction ;Basic probability theory and the summation convention. Case study: Birthdays Basic probability theory ;Riemann Sums. ;The fundamental theorem of Calculus (part I). Case study: Dam deconstruction. ; The fundamental theorem of Calculus ;Integration by substitution (part I) Case study: The IQ of a population. ;Integration of rational functions. Case study: The Logistic Equation. ;Integration by parts (part I) Case study: How fast are molecules moving? The Maxwellian distribution ;Integration of trigonometric functions Case study: Estimating natural energy resources ;Rectification of curves Case Study: TBD ;Improper integrals Case study: TBD ;Taylor Expansions Case study: TBD .

### Introduction to Analysis

Mathematical theory for the fundamental calculus concepts,  sequences and limits, continuous functions, and derivatives. Midterm solution homework solution Lectures note  Textbook:Kenneth Ross, Elementary Analysis: The Theory of Calculus

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