SPRING 2025 - MATH 21B - ENGINEERING CALCULUS

This is a rough outline of when topics will be covered and will be edited as the term progresses.
Exam dates will not change.
DayDateTopicsHomework:
MondayMar 315.1 Areas5.1: 1,3,6,10,12,19.
WednesdayApr 25.2 Summation
FridayApr 45.3 Definite Integrals
MondayApr 75.4 Fundamental Theorem of Calculus
WednesdayApr 95.5 Indefinite Integrals
FridayApr 115.6 Substitution
MondayApr 14Review
WednesdayApr 16Midterm I
FridayApr 188.1-8.2 Integration by Parts
MondayApr 218.3-8.4 Integration and Trig
WednesdayApr 238.5 Integrating Ratios
FridayApr 258 Integration Methods
MondayApr 286.1 Volume via Slices
WednesdayApr 306.2 Volume via Shells
FridayMay 26.3 Curve Length
MondayMay 5Review
WednesdayMay 7Midterm II
FridayMay 96.4 Surface Area
MondayMay 126.5 Work and Fluid Forces
WednesdayMay 146.6 Moments and Centers of Mass
FridayMay 167.2 Exponentials and Differential Equations
MondayMay 198.8 Improper Integration
WednesdayMay 2111.1-11.2 Calculus on Curves
FridayMay 23Review
MondayMay 26HOLIDAY: Memorial Day
WednesdayMay 28Midterm III
FridayMay 3011.3 Polar Coordinates
MondayJun 211.4-5 Length in Polar Coords
WednesdayJun 4Review
TuesdayJun 10 Final: 6:00-8:00 pm

Lecture: Eric Babson, babson@math.ucdavis.edu.
Mondays, Wednesdays and Fridays at 3:10 in California Hall.
Sections:
B01: Kenton Ke on Tuesdays at 5:10 in 1020 Wickson Hall.
B02: Kenton Ke on Tuesdays at 6:10 in 207 Wellman Hall.
B03: Regina Zhou on Tuesdays at 5:10 in 140 Physics Building.
B04: Regina Zhou on Tuesdays at 6:10 in 217 Olson Hall.
B05: Soyeon Kim on Tuesdays at 7:10 in 207 Wellman Hall most days but zoom 9293451331 on April 1.
B06: Soyeon Kim on Tuesdays at 8:10 in 1132 Bainer Hall most days but zoom 9293451331 on April 1.
B07: Nathalie Ndigaya on Tuesdays at 6:10 in 140 Physics Building.
B08: Kaia Smith on Tuesdays at 7:10 in 3211 Teaching Learning Complex.
B09: Hadj Kerrouchi on Tuesdays at 7:10 in 130 Physics Building.

Calculus Room: Math 21ABCD Calculus Room , where TAs are available to answer your questions.

Text: Any calculus text, such as Thomas' Calculus: Early Transcendentals (13th+ edition).

Exams: One sheet of notes (both sides) is allowed.

Grades:: There will be 400 pts from 3 midterms and a final. One midterm will be dropped. The final will be half or a third of the grade - whichever is higher [more explicitly: The midterms will each have 100 points and the final will have 200 points. Your score will be the larger of (Ma+Mb+F) or (2/3)(2Ma+2Mb+F) where Ma and Mb are your two highest midterm scores.]
D-DD+C-CC+B-BB+A-AA+
133150183200217250267283317333350383

Homework: Problems are listed for each lecture and due at the end of the following week. They will not be collected. Nobody has ever learned mathematics without working out a great many exercises. If a section seems opaque work more similar problems. Problems are from the 14th edition of Thomas' Calculus: Sec 4.8 - 5.6, Sec 6.1 - 6.6, Sec 7.1 - 8.7 and Sec 8.8 - 11.4.

Answers: Answers to all odd problems from the previous edition. Thanks to Dr Kouba for the detailed solutions to these problems including those assigned from sections: 4.8, 5.1 and 5.2, 5.3, more 5.3 and 5.4, 5.5, 5.6, 6.1, 6.2, 6.3, 6.4, 6.5, more 6.5, 6.6, 7.1, 7.2, 8.1, 8.2, 8.3, 8.4, 8.5, 8.7, 8.8, 11.1, 11.2, 11.3 with six extra and 11.4.

Course Outline: The focus of MAT 21B is on integration. The relationship between differentiation (MAT 21A) and integration is the Fundamental Thoerem of Calculus which continues after three centuries to have enormous impact in engineering, science and mathematics. After defining integrals and discussing the fundamental theorem this course will look at some methods for computing integrals. Despite their close link integrals turn out to be much harder to find than derivatives. The course will then cover a range of applications.