Advanced Calculus for Engineering [MATH 421] (Section 01), Spring 2016

General Information

Exam Dates

Teaching Assistant

Catalog Description

This course covers Laplace transforms, numerical solution of ordinary differential equations, Fourier series, and separation of variables method applied to the linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation).


The main prerequisite will be CALC4, which at Rutgers means either MATH 244, 252, or 292, i.e. differential equations. I will assume you have familiarity with basic calculus techniques, including calculus in more than one dimension (although I may spend a lecture or two reviewing some concepts). You will also be assumed to have some background in linear algebra in two and three dimensions; however I will spend some time (2-3 weeks, see the Tenative Schedule below) on vectors and matrices in higher dimensions (Chapter 8 in the textbook).


Your grade will be determined by the following distribution:

Final Exam 30%
Midterm I 25%
Midterm II 25%
Quizzes 20%
Standard grading cutoffs apply (A ≥ 90%, 80% ≤ B < 90%, etc.), but will possibly be adjusted (in the student’s favor only) for “borderline cases” and in the case I deem a curve necessary.

Exams The Final Exam will take place during the Exam week; it appears we are scheduled for May 10th, from 8-11 pm. Note that it will be cumulative, but possibly more heavily weighted to the material since Midterm II. The other two exams will take place in class, and will be announced at least two weeks before their administration. In general they will be closed book, and no calculators or other electronic devices will be permitted. I will provide a "cheat sheet," which will have some common formulas on it (for example, the Laplace transform of some standard functions), and which you will have access to before the exam.

Homework Suggested homework problems will be posted on the Course Calendar for each lecture. Note that homework will NOT be collected or graded, but is intended for practice for quizzes and exams, and should be considered representative of the type of problems to expect. To gain a thorough understanding of the material, doing ALL of the suggested problems is strongly encouraged.

Quizzes Quizzes will be given at the end of class each Thursday, (excluding the first week and possibly exam weeks), and will take no more than 20 minutes. The problems in each quiz will come directly from the previous two lecture's suggested homework problems (see the Course Calendar). Each will be weighed equally, and I will drop your two lowest scores.

Tenative Schedule

Math 421 is oriented toward students in Chemical & Biochemical Engineering and Mechanical & Aerospace Engineering. It develops mathematical tools used in upper-level engineering courses in these areas, and covers some fundamental techniques that are pervasive in science and engineering. In this course, I plan to cover four major topics: Laplace transforms (Chapter 4), linear algebra (Chapter 8), Fourier series (Chapter 12), and classical partial differential equations (PDEs) from physics (Chapter 13 and 14). Along the way, I will probably incorporate some additional concepts from vector calculus that you may not have encounteed in CALC3. A rough timeline (in number of lectures) is given below:

Laplace transforms 6 lectures
Linear algebra 6 lectures
Fourier series 6 lectures
Classical partial differential equations (PDEs) 8 lectures
Of course, this is just an approximation. For the most up-to-date information, as well as reading and homework assignments, see the Course Calendar. I will also post the quizzes (after they have been administered) here. Solutions (to quizzes and exams) will appear on Sakai .

Absences and Make-ups

Students are expected to attend all classes; if you expect to miss one or two classes, please use the University absence reporting website to indicate the date and reason for your absence. An email is automatically sent to me. Please note that there will be no make-ups for quizzes or exams. In cases of a justified and documented absence (for a medical or family emergency - and I was contacted before the exam) the weight of the missed exam will be shifted to the Final Exam.


I will use Sakai for email contact, as well as to post solutions to quizzes and exams. All enrolled students should have automatic access to the site after logging in to Sakai. Make sure to frequently check your email associated to your Sakai account.