Intermediate Calculus I MAT 226
Vector Calculus: Vectors in two and three dimensions, parametric equations and tangent/velocity vectors, equations of lines and planes, functions of several variables, partial differentiation, gradients, maximization, Lagrange multipliers, multiple integration and line integrals. Note: topics from the course description in the bulletin (e.g. power series) are now covered in Calculus II.
The webpage for calculus syllabi is http://comet.lehman.cuny.edu/calculus.
Prerequisite: MAT 175- MAT 176 (grades of C+ and up strongly recommended) All students are recommended to attend the review sessions of Calculus I and Precalculus given by the department in the second week of class. Weekly review homeworks are given in italics below.
Text same as MAT 175:
Larson, Hostetler and Evans, Calculus
Early Transcendental Functions, Houghton Mifflin, 4th Edition.
Textbook has a Webpage at http://college.hmco.com/mathematics/larson/calculus_early/4e/student_home.html
A Workbook by
Professor Petridis is available at http://comet.lehman.cuny.edu/petridis/226reader.pdf .
Note: In the 3rd edition of this same text most, but not all, material and exercises are just “shifted one chapter down”, e.g. Section 12.5 in the 4th edition corresponds to Section 11.5 in the 3rd edition.
Syllabus: (and suggested minimal homework)
Lesson I: Vectors, Plotting
in 3D, 11.1-11.2
(11.1/ 1, 5, 13, 21, 23, 33, 43. 11.2/ 1,3,5,11,29, 33, 37, 65.)
Lesson II: Dot and Cross Products 11.3-11.4
(11.3/ 3, 9, 17, 21, 47, 77. 11.4/ 1, 3, 5, 9, 11, 35, 47, 63.) Review
HW: Differentiation Chapter 3
Lesson III: Parametric Equations and Polar Coordinates 10.2, 10.4
(10.2/ 1,3,15, 39, 41, 42, 69. 10.4/ 1, 11,21,25,27, 29, 33, 35, 37.)
Lesson IV: Lines and Planes 11.5
(11.5/ 1, 3, 5, 11, 13, 19, 25, 27,
33, 37, 45, 51, 81.)
Lesson V: Hyperboloids, Paraboloids 11.6
(if time)
(11.6/ 1, 3, 5, 7, 9, 11, 23.) Review
HW: limits 2.2-2.4
Lesson VI: Cylindrical and Spherical Coordinates 11.7
(11.7/ 5, 11, 15, 17, 23, 27, 39,
43, 45, 53.)
Lesson VII: Catch-up Lesson
Review HW: Product rule 3.1-3.3 (3.2/ex2, ex3, ex5, ex6, ex7, ex8, ex9)
Lesson VIII: Vector valued functions, limits and continuity 12.1
(12.1/ 9, 11, 15, 17, 19, 21, 23,
59, 69.)
Lesson IX: Differentiation 12.2
(12.2/ 1,5,11, 17, 19, 41, 49, 59,
61 41.) Review HW: Chain Rule 3.4
Lesson X: Velocity and Acceleration, 12.3
(12.3/ 1, 3, 5, 9, 15, 17, 45, 47.)
Lesson XI: Tangent Vectors and Arc length 12.4-12.5
(12.4/ 5, 7, 13, 23. 12.5/
5, 7, 9, 11. ) Review HW: Surfaces 11.6
Lesson XII: Functions of several variables 13.1
(13.1/ 11, 13, 17, 19, 21, 27, 29, 31, 33, 35, 37, 67, 79.)
Lesson XIII: Level sets, 13.1,
(13.1/ 45, 47, 49, 51, 53, 69, 71,
73, 83, 85, 87.)
Review HW: Dot products and planes 11.3-11.5
Lesson XIV: Partial derivatives 13.3,
(13.2 if time)
(13.3/ 1, 3, 5, 7, 19, 25, 29, 33,
35, 51, 55, 59.)
Lesson XV: Gradients 13.6
(and the chain rule 13.5)
(13.6/ 3, 15, 29, 37, 51, 55 (sketch
and check), 59 (sketch and check), 63, 71
Read in 13.5: example 1, example 3, Thm 13.7, example 4; Do 13.5/ 1, 5, (7, 9))
Review HW: Extrema in One Variable 4.1
Lesson XVI: Tangent Planes 13.7
(go over theorems 13.6 and 13.7 in 13.5)
(13.7/ 5, 7, 11, 13, 15, 17, 55.)
Lesson XVII: Extrema and Saddle Points 13.8
(13.8/ 1, 9, 13, 27, 31, 37, 45.) Review
HW: for midterm
Lesson XVIII: Maximizing Profit 13.9
(if time) as a review
( Read example 5 of 13.8, do 13.8/53, 55, 59.
Read examples 1 and 2 of 13.9 and
do 13.9/ 1, 3, 19, 21 read example 3
of 13.9 and do 27 and 29. )
Lesson XIX: Midterm Exam
Review HW: Definition of
Integration 5.2-5.3
Lesson XX: Lagrange Multipliers 13.10
(Do examples in 13.10 and check yourself, 13.10/
5, 13,)
Lesson XXI: More Lagrange Multipliers 13.10
(13.10/ 15, 17, 25) Review HW:
Techniques of Integration 5.5
Lesson XXII: Iterated Integrals and Area 14.1
( 14.1/ 1, 3, 5, 7, 9, 11, 15, 21,
27, 29, 31, 39, 41, 43, 45, 47, 49, 53, 59 )
Lesson XXIII: Double Integrals 14.2
(14.2/ 7, 9,11,13, 15, 17, 19.)
Lesson XXIV: More integration 14.2
(14.2/ 23, 25, 49, 51, 53, 55, 61,
(63, 65) ) Review HW: Polar Coordinates 10.4
Lesson XXV: Integration and polar coordinates 14.3
( 14.3/ 9, 13, 15, 17, 23, 33, 55, 57 ) Review HW:
Vector-valued functions 12.2-12.3
Lesson XXVI: Vector Fields and Line Integrals 15.1-15.2
(15.1/ 1, 3, 5, 7, 9, 11, 21, 23,
35. 15.2/ 1, 3, 7, 13, 27, 35.) Review
HW: prep for final
Lesson XXVII: Path independence and Green’s Theorem 15.3-15.4 (if time)
(15.3/1, 5, 11, 25, 31. 15.4/ 1, 7, 11, 13, 21.)
Lesson XXVIII: Last class: Review for final