**Elementary Calculus and its Applications**

**Textbook:** ** Calculus** by Elliot Gootman, published by Barron’s

Lecture Notes and Video Lectures || Exams with answer

**Advanced Calculus For Engineers**–Dr.Z’s

**Lecture Notes**

## Calculus I HandOuts | Calculus I Attendance Quizes with Solution| Calculus II HandOuts and more

**Click her**

## Mathematical Methods I Fall2013

**Textbook:** W.Kaplan,2003, Advanced Calculus,Fifth Edition,Pearson

Lecture Notes on Mathematical Methods

- sample.tex: ascii file in LaTeX format
- sample.figure.eps: graphics file to be saved as sample.figure.eps and used in conjuntion with sample.tex
- compiled version of sample LaTeX file in .pdf format
- passage from Gleick
- sample mathematica file which solves an ODE numerically and plots the result
- pplane8.m matlab software, pplane8, to plot phase plane dynamics
- pplane2014b.m matlab software, pplane2014b, to plot phase plane dynamics

Other Resources

- General Interest
- Wolfram MathWorld This is one of the best serious resources for advanced mathematics knowledge on the web.
- Mathematics Genealogy Project
- PBS’s Nova on Fermat’s last theorem
- PBS’s Nova on chaos
- The Secret Life of Chaos, BBC documentary
- Mathematicians’ birthplaces
- Proof , Fine 2006 movie with a reasonably accurate depiction of the culture of mathematicians in the 21st century; see AMS review
- Good Will Hunting, Academy Award winning movie featuring applied mathematicians
- G. Gould playing J.S. Bach’s Contrapunctus 4 from The Art of Fugue
- Bach’s Gigue from French Suite Number 5, Part 2, BWV 816
- G. Gould playing Bach’s Brandenburg Concerto Number 5, Allegro
- T. Koopman playing Bach’s Little Fugue in G Minor, BWV 578
- Tutorial on Mandelbrot sets
- Julia and Mandelbrot Sets

- Software Tools
- LaTeX information
- Wolfram Research Homepage—Mathematica information
- MathWorks, Inc. Homepage—MATLAB information
- Waterloo Maple, Inc., Homepage—maple information
- UNIX help

- Professional Societies
- Departments, Institutes, Centers, and Agencies
- Bologna U., Research Center of Applied Mathematics
- U. British Columbia, Institute of Applied Mathematics
- Brown U., Division of Applied Mathematics
- Cambridge U., Department of Applied Mathematics and Theoretical Physics
- Cambridge U., Isaac Newton Institute for Mathematical Sciences
- Cal Tech, Department of Computing + Mathematical Sciences
- Colorado-Boulder, Department of Applied Mathematics
- Cornell U., Center for Applied Mathematics
- ETH Zurich, Seminar for Applied Mathematics
- U. Minnesota, Institute for Mathematics and its Applications
- NSF, Directorate for Math and Physical Sciences
- NYU, Courant Institute of Mathematical Sciences
- Northwestern U., Engineering Sciences and Applied Mathematics
- U. Notre Dame, Department of Applied and Computational Mathematics and Statistics
- RPI, Department of Mathematical Sciences
- SUNY-Stony Brook, Department of Applied Mathematics and Statistics
- Virginia Tech, Interdisciplinary Center for Applied Mathematics
- U. Washington, Department of Applied Mathematics
- U. Western Ontario, Department of Applied Mathematics

- Periodicals and Archive Journals
- Quarterly Journal of Mechanics and Applied Mathematics
- SIAM Journal on Applied Mathematics
- SIAM Journal on Applied Dynamical Systems
- SIAM Journal on Matrix Analysis and Applications
- SIAM Journal on Scientific Computing
- SIAM/ASA Journal on Uncertainty Quantification
- SIAM Review
- SIAM Journal on Optimization
- SIAM Journal on Control and Optimization

Department of Aerospace and Mechanical Engineering Universityof Notre Dame

**Calculus I Pre**

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

*Math*

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

Homework solution , Exam Solutions , Practice Exam and Solutions , Worksheet , Basic Derivative Formulas and Trig Identities , handouts-Lectures

**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 Taught**at *Lake Tahoe Community College*, by Larry Green

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

CAHSEE (California High School Exit Exam Prep)

*Advanced Engineering Mathematics*

*Advanced Engineering Mathematics*

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.

**; Existence and uniqueness theory for ordinary differential equations ; Systems of linear differential equations;**

*Exact differential equations***with constant coefficients , Fundamental systemsMethods**

*Solving homogeneous systems*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,

**; Hamiltonian systems;**

*Nonlinear systems of differential equations***.**

*The mathematical pendulum*

** Calculus Book** with

**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,**

*Video Lecture**.*

**calculus exam with solution**Recurrent Problems, Sums, ** Integer functions**, Number Theory,

*Binomial Coefficients*, Special numbers, Classical

*Discrete Mathematics*.

*HOMEWORK 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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