Schedule
A sample schedule and course information for Honors Calculus
Department of Mathematical Sciences
Indiana University - Purdue University Fort Wayne (IPFW)
Honors Calculus - Sample Schedule
Page numbers refer to course books:
WIF = the book "Who is Fourier? A Mathematical Adventure"
LN = the Lecture Notes
Calculus I - MA 163H
Week 1
Review of Trigonometric Functions, Real Numbers, Inequalities, and Rational Numbers
WIF 1 - 68
LN 7 - 11
Week 2
Fourier Coefficients, Number Sets
WIF 69 - 113
LN 11 - 14
Weeks 3 - 4
Discrete Fourier Expansion, Spectrum, Review of Logarithm and Exponential Functions, Sequences and Limits of Sequences
WIF 114 - 163
WIF 300 - 305
LN 14 - 37
Weeks 5 - 6
Functions
LN 38- 56
Weeks 6 - 10
Differentiation
WIF 164 -217
WIF 305 - 313
LN 56 - 78
Weeks 11 - 12
Analysis of Functions of a Single Variable, Extrema, Related Rate Problems, and
L'Hospital's Rule
LN 78 - 99
Weeks 13 - 15
Integrals
WIF 218 - 258
LN 100 - 133
Week 15
Review
Calculus II - MA 164H
Weeks 1 - 2
Projection and Orthogonality, Review of Integrals, Integration by Substitution
WIF 259 - 294
LN 7 - 45
Weeks 3 - 4
The Numbers e and i, Integration by Parts
WIF 295 - 324
LN 46 - 53
Weeks 5 - 6
Euler's Formula, Improper Integrals
WIF 325 - 354
LN 53 - 64
Week 7
Review of Sequences, Series, Absolutely Convergent Series
LN 163H: 14 -35
LN 164H: 64 - 74
Weeks 8 - 9
Complex Number Representation of Fourier Series and Fourier Coefficients, Series with Positive Terms, Stirling's Formula
WIF 355 - 370
LN 74 - 82
Weeks 10 - 11
The Fourier Transform and Uncertainty of Waves, Series of Functions, Power Series, MacLaurin and Taylor Series
WIF 371 - 390
LN 83 - 96
Week 12
Binomial Series, Integration with Series
LN 96 - 109
Weeks 13 - 15
The FFT Method, Fourier Series
WIF 391 - 410
LN 109 - 120
Week 15
Review
How to use the book "Who is Fourier?" (WIF) and the Lecture Notes (LN)?
Students are expected to read assigned sections to be presented in class at home, and make sure they understand the text fully and completely. WIF will be used more for the intuitive understanding of the mathematical concepts and for the presentation of Fourier analysis that is not covered in LN. LN provides the analytical formalization of the mathematical concepts, theorems, computations, and methods. There are proofs in LN, which are an important integral part of the course. Students are supposed to understand these proofs, but they are not required to memorize or repeat them. The instructor will explain these proofs in class, and help students understand them. Some of the problems are based on these proofs as they are in any standard calculus book. Students are required to learn the theorems, they should be able to recall the conditions of the theorems, and be able to use them for solving exercises and problems.Some of the theorems are stated without a proof. Students can get extra credit any time by proving those theorems on their own, or by learning the proofs from other books. (For some of these theorems, LN has a hint to guide students to prove them.) In order to get the extra credit, students are not required to present the proofs, but they are required to explain the steps of the proofs to the instructor by using their own notes. The instructor will be happy to help students with the extra credit, and willing to help explain some of the steps that are hard for a student to understand.
The projects are designed for group work, but students who feel more comfortable doing individual work will not be forced to participate in group work. Students are allowed to choose their own groups, but a group cannot contain more than three students. Groups (or individuals) are required to do the problems and present them to the instructor either in written form or by oral presentation. Each member of the group must be ready for the presentation. During any presentation students are allowed to use their own written notes. The instructor may ask for a presentation even if he collects written answers. Some of the problems of these projects are challenging, so the instructor is happy to give extra help for groups (or individuals) with no penalty at all. The only thing that is expected from students in these help sessions is active participation. There are exercises in LN that are supposed to help students learn the standard drill skill. They are supposed to be done by each student, but they will not be collected or graded. Students can ask for help with these problems in class or during office hours. Because of time constraints, some integrals and integration techniques are covered in MA 163-H, some in MA 164-H. At the end of the MA 163-H LN there are some exercises that will be repeated in the Lecture Notes for MA 164-H. They will be assigned in MA 163-H only if they will be covered fully or partially.
Honors Calculus - Grades
The grades will consist of individual test grades (three of them, including a comprehensive final: 20%, 20%, 20%), a group project grade (20%), and an individual project grade (20%). The guaranteed cutoffs for the grades, in percentages are: 85%, 75%, 65%, and 60%, for A, B, C, and D, respectively. Students below but close to the guaranteed cutoff can earn extra credit by doing extra work in mathematics (see above).
The individual projects will be related to the student's major. In each project they need to analyze waves phenomena or they need to use the Fast Fourier Transform method. There are four projects listed at the end of some of the chapters of the Lecture Notes (LN). They are about topics that are informally covered by the book Who is Fourier (WIF), or that enhance the presentation of the LN.
