Multivariable Calculus | Michael Taylor. Math 233H is the honors section of Math 233, the third semester of calculus at UNC. It focuses on Multivariable Calculus. The text for this section will be: Multivariable Calculus Here is the syllabus In outline, here are the contents of the text: Chapter 1. Chapter 1 presents a brisk review of the basics in one variable calculus: definitions and elementary properties of the derivative and integral, the fundamental theorem of calculus, and power series.
Multidimensional calculus is done on multidimensional spaces, and Chapter 2 introduces tools useful for this study. Chapter 4 treats the derivative of a function of several variables, including higher derivatives and multivariable power series, and the inverse and implicit function theorems. Chapter 6 studies smooth surfaces in Euclidean space, and differential and integral calculus on such surfaces, and establishes a trio of fundamental integral identities known as the formulas of Gauss, Green, and Stokes.
Linear Algebra. Differential Calculus: From Practice to Theory - Milne Open Textbooks. To the Instructor 0.1 What Do Students Need From Calculus? 0.2 Some (Possibly Startling) Choices We’ve Made 0.3 Some Practical Advice 0.4 The TRIUMPHS Project 0.5 Rantings From the Cranky Old Guys in the Back of the Room 0.6 A Plea For Help Preface: Calculus is a Rock I. 1. 1.1 Using Letters Instead of Numbers 1.2 Substitution, or Making Things “Easy on the Eyes” 1.3 An “Easy” Problem From Geometry 1.4 Our advice, a synopsis 2. 2.1 Apologia 2.2 Some Preliminaries 2.3 The Laziness of Nature 2.4 Fermat’s Method of Adequality 2.5 Descartes’s Method of Normals 2.6 Roberval, Conic Sections, and the Dynamic Approach 2.7 Snell’s Law and the Limitations of Adequality 3. 3.1 Historical Introduction 3.2 The General Differentiation Rules 4. 4.1 Slopes and Tangents 4.2 Defining the Tangent Line 4.3 The Vomit Comet 4.4 Galileo Drops the Ball 4.5 The Derivative 4.6 Thinking Dynamically 4.7 Newton’s Method of Fluxions 4.8 Self-intersecting Curves and Parametric Equations 4.9 Bridges, Chains, Domes, and Telescopes 5. 5.9 Curvature.
How We Got from There to Here: A Story of Real Analysis - Milne Open Textbooks. Prologue: Three Lessons Before We Begin I: In Which We Raise a Number of Questions 1 Numbers, Real (R) and Rational (Q) 2 Calculus in the 17th and 18th Centuries 2.1 Newton and Leibniz Get Started 2.1.1 Leibniz’s Calculus Rules 2.1.2 Leibniz’s Approach to the Product Rule 2.1.3 Newton’s Approach to the Product Rule 2.2 Power Series as Infinite Polynomials 3 Questions Concerning Power Series 3.1 Taylor’s Formula 3.2 Series Anomalies II Interregnum Joseph Fourier: The Man Who Broke Calculus III In Which We Find (Some) Answers 4 Convergence of Sequences and Series 4.1 Sequences of Real Numbers 4.2 The Limit as a Primary Tool 4.3 Divergence 5 Convergence of the Taylor Series: A “Tayl” of Three Remainders 5.1 The Integral Form of the Remainder 5.2 Lagrange’s Form of the Remainder 5.3 Cauchy’s Form of the Remainder 6 Continuity: What It Isn’t and What It Is 6.1 An Analytic Definition of Continuity 6.2 Sequences and Continuity 6.3 The Definition of the Limit of a Function 6.4 The Derivative, An Afterthought.
Calculus Made Easy | Free Online Calculus Book | Abakcus. Mathematics Education | Department of Mathematics. Seminars Group overview The Mathematics Education group at its core consists of Education Leadership Stream faculty members, but includes others who are passionate about postsecondary teaching and have contributed in significant ways to the department's teaching mission. For example, the group has been instrumental in producing open educational resources (see links below) and has received much recognition for this work. Group activities include the Mathematics Education Research seminar, Lunch series on Teaching and Learning, curriculum development, and activities related to outreach and the scholarship of teaching and learning. For prospective students Graduate students who are passionate about teaching are encouraged to take MATH 599 and participate in our seminars and lunch series.
For prospective POSTDOCTORAL FELLOWS This section contains brief descriptions of potential projects for Teaching Project Postdoctoral Fellows. CLP Calculus Textbooks. How a book written in 1910 could teach you calculus better than several books of today [Calculus Made Easy, by Silvanus P. Thompson, 1910 - full text pdf or with the table of contents.
Calculus Made Easy. Calculus made easy : Thompson, Silvanus Phillips : Free Download, Borrow, and Streaming. Error 400 (Bad Request)!!1. Multivariable. Free Calculus Ebooks. Calculus. Topics in Calculus. AP Calculus BC Course Home Page. The AP Calculus BC Exam. Exam Content In 1956, 386 students took what was then known as the AP Mathematics Exam. By 1969, still under the heading of AP Mathematics, it had become Calculus AB and Calculus BC. The Calculus BC exam covers the same differential and integral calculus topics that are included in the Calculus AB exam, plus additional topics in differential and integral calculus, and polynomial approximations and series. This is material that would be included in a two-semester calculus sequence at the college level.
If students take the BC exam, they cannot take the AB exam in the same year because the exams share some questions. Multiple-Choice Questions For sample multiple-choice questions, refer to the Course Description. AP Calculus Course Description, Effective Fall 2012 (.pdf/2.28MB) AP Calculus Multiple-Choice Question Index: 1997, 1998 and 2003 AP Calculus Exams(.xls/144KB) Free-Response Questions Below are free-response questions from past AP Calculus BC Exams. 2013: Free-Response Questions. Calculus BC. Yet Another Calculus Text. CALCULUS.ORG. THE CALCULUS PAGE PROBLEMS LIST. Problems and Solutions Developed by : D.
A. Kouba And brought to you by : Beginning Differential Calculus : Problems on the limit of a function as x approaches a fixed constant limit of a function as x approaches plus or minus infinity limit of a function using the precise epsilon/delta definition of limit limit of a function using l'Hopital's rule ... Beginning Integral Calculus : Problems using summation notation Problems on the limit definition of a definite integral Problems on u-substitution Problems on integrating exponential functions Problems on integrating trigonometric functions Problems on integration by parts Problems on integrating certain rational functions, resulting in logarithmic or inverse tangent functions Problems on integrating certain rational functions by partial fractions Problems on power substitution Problems on integration by trigonometric substitution ...
Sequences and Infinite Series :