Text: Calculus (2Nd Edition), by W. Briggs, L. Cochran, and B. Gillett

MATH1710 – Calculus I Text: Calculus (2nd edition), by W. Briggs, L. Cochran, and B. Gillett

Course Delivery: This course is delivered on the MyLabsPlus (MLP) 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 MLP 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 CONTENT Prerequisite Quiz The MyMathLab course shell has a quiz covering prerequisite material from algebra and trigonometry.

2 Limits Instructors should spend most of the time on the 2.1 The Idea of Limits “core” sections 2.2 – 2.4 which provide the tools for the practical evaluation of limits as well as an 2.2 Definitions of Limits explanation of the important concept of a continuous 2.3 Techniques for Computing Limits function. 2.4 Infinite Limits If time permits the instructor may wish to introduce students to the formal “epsilon-delta” approach to 2.5 Limits at Infinity limits in section 2.7 2.6 Continuity 2.7 Precise Definitions of Limits (optional) 3 Derivatives This chapter contains the basic material of 3.1 Introducing the Derivative differential calculus and all sections should be covered thoroughly. The later sections (3.7, 3.8) as 3.2 Rules of Differentiation well as all of chapter 4 require a thorough 3.3 The Product and Quotient Rules understanding of the mechanics covered in 3.2 – 3.6. 3.4 Derivatives of Trigonometric Functions Spending a good deal of time in section 3.6 is advised as the chain rule is omnipresent and some of its uses 3.5 Derivatives and Rates of Change can be a little subtle for some students. 3.6 The Chain Rule Students also tend to find 3.8 difficult; pay special 3.7 Implicit Differentiation attention to showing students how to “set up” the problems. 3.8 Related Rates 4 Applications of the Derivative This opens by explaining how derivatives encode a 4.1 Maxima and Minima wealth of information about a function. This culminates in section 4.3 where the students learn to 4.2 What Derivatives Tell Us draw accurate sketches of graphs based on 4.3 Graphing Functions information gleaned from derivatives. However, don’t spend too much time for section 4.3. since 4.4 Optimization Problems every student has access to graphing tools. 4.6 The Mean Value Theorem Section 4.4 on optimization tends to be very difficult 4.7 L’Hopital’s Rule for students. Again one should take care to explain how the problems are “set up”. 4.8: Newton’s method In 4.7 be sure to warn students about illegitimate uses 4.9 Antiderivatives of L’Hospital’s Rule. Section 4.8 is requested to teach by Engineering department.

5 Integration The beginning of the chapter is an exposition of the 5.1 Approximating Areas Under Curves theory behind the integral calculus (Riemann sums). Students tend to find the complexity of the notation 5.2 Definite Integrals bewildering. Less time could be spent with explicitly 5.3 Fundamental Theorem of Calculus computing Riemann Sum (this skill is not used again in the calculus sequence). 5.4 Working with Integrals It will make the volume problems in chapter 6 “easier 5.5 Substitution Rule 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 This chapter opens with a short section focused on 6.1 Velocity and Net Change the meaning of the integral in a physical context. The remainder of the chapter puts the integral to work 6.2 Regions Between Curves solving problems of a geometric nature. 6.3 Volumes by Slicing Emphasis should be placed on what the author calls 6.4 Volumes by Shells 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).