Course Schedule and Homeworks

Note: Homeworks assigned in week 1,2,3 etc. will be subject of the quiz given online the week after. For example the quiz on Friday of the second week will be about the homework given duirng the first week .

Week 1 Introduction, two-dimensional vectors, dot products. Sections 1.1, 1.2.

Important: Discuss the polar coordinate representation of vectors and how to rotate a vector about the origin by a given angle (see the extra exercise on the list of homework problems for section 1.2)

Chapter 0:   Pg. 15  # 1, 3, 9, 11, 15, 17, 25, 36, 61, 63, 67, 71, 83, 87, 89, 91, 99, 101 


             Pg. 26  # 3, 4, 7, 9, 17, 23
             
Section 1.1: Pg. 53  # 3, 5, 9, 13, 17, 19, 21, 25, 27, 29

Section 1.2: Pg. 60  # 1, 5, 7, 13, 15, 17, 21, 25, 31, 35, 37,
                       41, 43, 51, 53, 55
                       Also be able to do the following problem:
		       Let A1 and B1 be the vectors (1,2) and (-3,1),
		       respectively. Let A2 and B2 be the vectors
		       obtained by rotating A1 and B1 by an angle of 
		       60 degrees in the counterclockwise direction.
		       Compute the vectors A2 and B2 and show that 
		       the dot product of A2 with B2 is the same
                       as the dot product of A1 with B1.
		       (Hint: express A1 and B1 in polar coordinates)

		       Answer: A2=(-1.232, 1.866) ;  B2=(-2.366, -2.098)

Week 2 Parameterized curves, (qualitative) definition of limit and the calculation of limits. Sections 1.3, 2.2, 2.3. Examples from Section 2.1 on tangent and velocity can be incorporated into Section 2.2 to motivate limits. The concepts of tangents and velocity will be revisited in later sections.

                       
Section 1.3  Pg. 68  # 1, 3, 7, 11, 15, 19, 25, 27, 29, 
                       31, 34
                       
Section 2.1  Pg. 78  # 1, 3, 5, 11

Section 2.2  Pg. 89  # 3, 5, 7, 13, 17, 21

Section 2.3  Pg. 99  # 3, 5, 6, 7, 13, 19, 23, 27, 39, 41
                       45, 55, 67, 71

Week 3 Limits at infinity, continuity, velocity. Sections 2.5, 2.6, 2.7. Note that the epsilon-delta definition (section 2.4) is skipped.

Section 2.5  Pg. 120 # 1, 3, 9, 15, 17, 23, 29, 33,  37, 39, 43, 47

Section 2.6  Pg. 133 # 3, 11, 17, 27, 29, 35, 45, 47

Section 2.7  Pg. 143 # 1, 3, 5, 9, 11, 15, 17, 21, 23

Week 4 Differentiation and rates of change. Sections 3.1, 3.2, 3.3. Note. Physics has requested that we cover antidifferentiation formulas along with differentiation formulas.

Section 3.1  Pg. 157 # 1, 5, 7, 13, 15, 23, 33, 34, 
                       37, 39, 41, 47, 51, 53
                       
Section 3.2  Pg. 168 # 3, 7, 9, 15, 19, 23, 29, 37, 39, 
                       43, 50, 53, 55, 61, 70, 72
             and Pg. 353 # 1, 3, 5, 9
             
Section 3.3  Pg. 178 # 3, 7, 9, 11, 13, 17, 23

----------------------------------------------------------------Exam 1

Week 5 Derivatives of the trigonometric functions, the chain rule and EXAM I (Thursday, covering thru 3.3). Sections 3.4, 3.5.

Section 3.4  Pg. 185 # 5, 7, 11, 15, 19, 21, 23, 27, 31, 33, 45
	     and Pg. 353 # 11, 13

Section 3.5  Pg. 192 # 3, 7, 11, 13, 27, 33, 49, 51, 57, 
                       59, 79, 80

Week 6 Implicit differentiation, derivatives of vector-valued functions, higher derivatives, tangents of parameterized curves. Sections 3.6, 3.7, 3.8, 3.9. The section on higher derivatives is very short and will be covered rapidly.

Section 3.6  Pg. 198 # 1, 5, 11, 13, 21, 25, 27, 33, 
                       35, 39, 45
                       
Section 3.7  Pg. 203 # 3, 5, 11, 13, 17, 21
                       
Section 3.8  Pg. 208 # 1, 2, 5, 11, 17, 31, 35, 43, 46, 49, 51

Section 3.9  Pg. 214 # 3, 5, 7, 9, 13, 17, 21

Week 7 Related rates, differentials and approximation, Newton's method Sections 3.10, 3.11, 3.12. Pay particular attention in section 3.11 to standard approximations, such as sin(x) ~ x and sqrt(1+x) ~ 1+x/2.

Section 3.10 Pg. 221 # 5, 7, 9, 11, 15, 17, 19, 23, 
                       27, 31, 33
                       
Section 3.11 Pg. 227 # 3, 9, 10, 14, 23, 27, 35, 36, 38, 39, 41, 45

Section 3.12 Pg. 232 # 1, 3, 7, 9, 13

Week 8 Exponential and inverse functions, logarithmic functions. Sections 4.1, 4.2, 4.3.

Section 4.1  Pg. 248# 3, 6, 7, 10, 17, 21, 25, 27, 29, 31, 35
                      43, 47, 49, 59

Section 4.2  Pg. 256  # 3, 5, 7, 11, 13, 15, 19, 23, 25, 31, 35

Section 4.3  Pg. 262  # 3, 7, 11, 19, 21, 25, 29, 39, 43, 45, 51
                        61, 70, 73, 79, 87

---------------------------------------------------------------Exam 2

Week 9 Derivatives of logarithms, exponential growth and decay, and EXAM II (Thursday, covering 3.4 - 4.3). Sections 4.4, 4.5 .

Section 4.4  Pg. 269  # 3, 7, 9, 13, 19, 27, 35, 39, 51, 59

Section 4.5  Pg. 274  # 3, 5a), 9, 11, 13, 15, 19, 21

 Week 10 Inverse trigonometric functions, L'Hospital's Rule, graphical interpretation
of the derivative.
Sections 4.6, 4.8, 5.1.

Section 4.6  Pg. 281  # 3, 9, 17, 23, 27, 31, 35, 45, 51, 53, 65, 66

Section 4.8  Pg. 295  # 3, 9, 13, 17, 19, 25, 39, 41, 47, 55, 57, 61, 65

Section 5.1  Pg. 305  # 1, 3, 5, 11, 13, 17, 19, 21






 Week 11 First and second derivative tests, applied Max/Min. 
Sections 5.2, 5.3, 5.5 (5.4
on curve sketching with technology will be done in lab).

Section 5.2  Pg. 312  # 3, 7, 11, 17, 19, 25, 27, 31, 37, 39, 41, 43, 45

Section 5.3  Pg. 322  # 1, 5, 7, 9, 13, 17, 19, 21, 35, 43, 45

Section 5.5  Pg. 337  # 1, 5, 7, 9, 13, 17, 19, 23, 27, 29, 31, 33, 39
	

 Week 12 Antiderivatives,
Riemann sums, and the definite integral.

Sections 5.7, 6.1, 6.2, 6.3


Section 5.7  Pg. 353  # 3, 7, 9, 15, 17, 21, 23, 27, 31, 37, 39, 41,
			43, 45, 49, 59, 61, 65, 71, 73, 79



Section 6.1  Pg. 368  # 5, 9, 19, 25, 41 b), 43  Note: it is not 
              necessary to memorize the summation 
              formulas 


Section 6.2  Pg. 377  # 1, 5, 13, 15 (at least be able to set up the
              the Riemann sum for  13 and 15), 23

Section 6.3  Pg. 386  # 7, 11, 17, 33, 35, 45, 47, 53, 55


 Week 13 The Fundamental Theorem of Calculus. 
(in the fall, Thanksgiving falls this week.) Section 6.4.

Section 6.4  Pg. 397  # 1, 3, 7, 9, 11, 19, 23, 27, 31, 41, 47, 51, 57, 
               73, 77, 79, 83, 93, 95


---------------------------------------------------------------Exam 3
 Week 14 Substitution rule and EXAM III
 (Tuesday, covering 4.4 - 6.4).Section 6.5.

Section 6.5  Pg. 407  # 5, 7, 11, 19, 27, 35, 39, 43, 47, 55, 61, 65

 Week 15 Review for FINAL. Last day of class
is Tuesday. Note that the last week of class has 
redefined day(s). See  Important Dates  for details.