MATH1710 – Calculus I
Text: Calculus (2nd edition), by W. Briggs, L. Cochran, and B. Gillett
Course Delivery: This course is delivered on the MyMathLab platform. Some of the homework assignments are on the online platform. In addition students complete written assignments consisting of more elaborate problems. Students can access the entire textbook (along with a plethora of learning resources) on the platform as well. In addition MML and the lecture, the students will attend recitation sections with a TA.
The online textbook has many interactive figures some of which the instructor might wish to demonstrate in the classroom (notably in the sections regarding Riemann sums).
Sections which are particularly crucial for later sections and later courses have been underlined.
CH / TITLE/SECTIONS / CONTENTPrerequisite Quiz / The MyMathLab course shell has a quiz covering prerequisite material from algebra and trigonometry.
2 / Limits
2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definitions of Limits (optional) / Instructors should spend most of the time on the “core” sections 2.2 – 2.4 which provide the tools for the practical evaluation of limits as well as an explanation of the important concept of a continuous function.
If time permits the instructor may wish to introduce students to the formal “epsilon-delta” approach to limits in section 2.7
3 / Derivatives
3.1 Introducing the Derivative
3.2 Rules of Differentiation
3.3 The Product and Quotient Rules
3.4 Derivatives of Trigonometric Functions
3.5 Derivatives and Rates of Change
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Related Rates / This chapter contains the basic material of differential calculus and all sections should be covered thoroughly. The later sections (3.7, 3.8) as well as all of chapter 4 require a thorough understanding of the mechanics covered in 3.2 – 3.6.
Spending a good deal of time in section 3.6 is advised as the chain rule is omnipresent and some of its uses can be a little subtle for some students.
Students also tend to find 3.8 difficult; pay special attention to showing students how to “set up” the problems.
4 / Applications of the Derivative
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.6 The Mean Value Theorem
4.7 L’Hopital’s Rule
4.8: Newton’s method
4.9 Antiderivatives / This opens by explaining how derivatives encode a wealth of information about a function. This culminates in section 4.3 where the students learn to draw accurate sketches of graphs based on information gleaned from derivatives. However, don’t spend too much time for section 4.3. since every student has access to graphing tools.
Section 4.4 on optimization tends to be very difficult for students. Again one should take care to explain how the problems are “set up”.
In 4.7 be sure to warn students about illegitimate uses of L’Hospital’s Rule.
Section 4.8 is requested to teach by Engineering department.
5 / Integration
5.1 Approximating Areas Under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
5.5 Substitution Rule / The beginning of the chapter is an exposition of the theory behind the integral calculus (Riemann sums). Students tend to find the complexity of the notation bewildering. Less time could be spent with explicitly computing Riemann Sum (this skill is not used again in the calculus sequence).
It will make the volume problems in chapter 6 “easier to swallow”
Competence at change of variable (substitution) is vital for future courses. Accordingly section 5.5 should be covered slowly and thoroughly with plenty of examples.
6 / Applications of Integration
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volumes by Slicing
6.4 Volumes by Shells / This chapter opens with a short section focused on the meaning of the integral in a physical context. The remainder of the chapter puts the integral to work solving problems of a geometric nature.
Emphasis should be placed on what the author calls the “slice and sum” approach. This shows the typical manner in which integration formulas arise (not only in mathematics proper but in related disciplines as well).