Course Overview
|
Course Synopsis
|
Single variable calculus which is what we begin with can deal with motion of an object along a fixed path. The more general problem when motion can take place on a surface or in space can be handled by multivariable calculus. So single variable calculus is the key to the general problem as well. The topics which will be covered in the course are Real numbers set theory intervals and inequalities Lines functions and graphs Limits and Continuity Differentiation Integration and Sequence and Series. The study of calculus is normally aimed at giving you the mathematical sophistication to relate to such more advanced work. Calculus and Analytical Geometry MTH101 is prerequisite course for Calculus II MTH301.
|
Course Learning Outcomes
|
At the end of the course you should be able to
- Understand and manipulate real numbers solve inequalities and represent solutions on the real number line with proficiency
- Demonstrate proficiency in graphing equations on the Cartesian plane calculating distances between points and graphing various types of functions
- Understand limits intuitively and rigorously analyze continuity of functions and solve related problems with proficiency
- Calculate derivatives using various techniques and solve problems related to rates of change tangent lines extrema and the Mean Value theorem
- Understand integration concepts evaluate definite and indefinite integrals and apply integration to find areas volumes lengths of curves and work done
- Apply the First and Second Fundamental Theorems of Calculus to evaluate definite integrals and find antiderivatives
- Evaluate improper integrals apply L39Hopital39s Rule to analyze indeterminate forms and understand sequences and series concepts including convergencedivergence tests
- Find Taylor and Maclaurin series expansions of functions and use them to approximate function values with proficiency
|
Course Calendar
|
|
|
Week 01
|
1
|
Real Numbers, Intervals, Inequalities.(Lecture # 1)
|
|
2
|
Absolute Value.(Lecture # 2)
|
|
3
|
Coordinate Planes and Graphs (Lecture#3)
|
Week 02
|
5
|
DIstance; Circles, Quadratic Equations(Lecture#5)
|
Week 03
|
7
|
Operations on Functions(Lecture#7)
|
|
8
|
Graphing Functions(Lecture#8)
|
|
9
|
Limits (Intuitive Introduction) (Lecture#9)
|
Quiz No 1
Week 04
|
10
|
Limits (Computational Techniques)(Lecture#10)
|
|
11
|
Limits (Rigorous Approach)(Lecture#11)
|
|
12
|
Continuity(Lecture#12)
|
Week 05
|
13
|
Limits and Continuity of Trignometric Functions(Lecture#13)
|
|
14
|
Tangent Lines, Rates of Change(Lecture#14)
|
|
15
|
The Derivative(Lecture#15)
|
Week 06
|
16
|
Techniques of Differentiation(Lecture#16)
|
|
17
|
Derivatives of Trigonometric Functions(Lecture#17)
|
|
18
|
The Chain Rule(Lecture#18)
|
Quiz No 2
Week 07
|
19
|
Implicit Differentiation(Lecture#19)
|
|
20
|
Derivatives of Inverse Functions(Lecture#20)
|
|
21
|
Applications of Differentiation(Lecture#21)
|
Week 08
|
22
|
Extreme Maxima(Lecture#22)
|
Mid-Term Examination
|
23
|
Maximum and Minimum Values of Functions(Lecture#23)
|
|
24
|
Newton's Method, Rolle's Theorem and the Mean Value Theorem(Lecture#24)
|
Week 09
|
25
|
Integrations(Lecture#25)
|
|
26
|
Integration by Substitution(Lecture#26)
|
|
27
|
Sigma Notation(Lecture#27)
|
Week 10
|
28
|
Area as Limit(Lecture#28)
|
|
29
|
Definite Integral(Lecture#29)
|
|
30
|
First Fundamental Theorem of Calculus(Lecture#30)
|
Quiz No 3
Week 11
|
31
|
Evaluating Definite Integral by Substitution(Lecture#31)
|
|
32
|
Second Fundamental Theorem of Calculus(Lecture#32)
|
|
33
|
Area between two curves(Lecture#33)
|
Week 12
|
34
|
Volumes by slicing; Disks and Washers(Lecture#34)
|
|
35
|
Volumes by Cylindrical shells(Lecture#35)
|
Quiz No 4
|
36
|
Length of Plane Curves(Lecture#36)
|
Week 13
|
37
|
Area of Surface of Revolution(Lecture#37)
|
|
38
|
Work and Definite Integral(Lecture#38)
|
|
39
|
Improper Integral.(Lecture#39)
|
Quiz No 5
Week 14
|
40
|
L'Hopital's Rule(Lecture#40)
|
|
41
|
Sequences and Monotone Sequences(Lecture#41)
|
|
42
|
Infinite Series(Lecture#42)
|
Week 15
|
43
|
Additional Convergence tests(Lecture#43)
|
|
44
|
Alternating Series ; Conditional Convergence(Lecture#44)
|
|
45
|
Taylor and Maclaurin Series(Lecture#45)
|
Final-Term Examination
|
|
|