# |
Learning Outcomes |
1 |
Students will be able to compute limits and to carry out some basic proofs about limits and continuty. |
2 |
Students will be able to compute derivates and to use it in applications such as computing rates of change, finding extreme values. |
3 |
Students will be able to sketch graphs of functions by finding intervals of increase /decrease, concavity and asymptotes. |
4 |
Students will be able to use transcendental functions including logarithms, exponentials and inverse trigonometric functions effectively. |
5 |
Students will be able to compute integrals by the Riemann Sum defintion and use it to make approximations. |
6 |
Students will be able to make use of various techniques to compute proper and improper integrals. |
# |
Subjects |
Teaching Methods and Technics |
1 |
Ch 0: Preliminaries
0.1 Real Numbers and the Real Line
0.2 Cartesian Coordinates in the Plane
0.3 Graphs of Quadratic Equations
0.4 Functions and Their Graphs
0.5 Combining Functions …
0.6 Polynomials and Rational Functions
0.7 The Trigonometric Functions |
lecturing, discussing, problem solving |
2 |
Ch 1: Limits and Continuity
1.2 Limits of Functions
1.3 Limits at Infinity and Infinite Limits
1.4 Continuity
|
lecturing, discussing, problem solving |
3 |
1.4 Continuity
1.5 The Formal Definition of Limit
Ch 2: Differentiation
2.1 Tangent Lines and Their Slope
2.2 The Derivative
2.3 Differentiation Rules
|
lecturing, discussing, problem solving |
4 |
2.4 The Chain Rule
2.5 Derivatives of Trigonometric Functions
2.6 Higher-Order Derivatives
2.8 The Mean-Value Theorem
|
lecturing, discussing, problem solving |
5 |
2.9 Implicit Differentiation
Ch 3: Transcendental Functions
3.1 Inverse Functions
3.2 Exponential and Logarithmic Functions
|
lecturing, discussing, problem solving |
6 |
3.3 The Natural Logarithm and Exponential
3.5 The Inverse Trigonometric Functions
3.6 Hyperbolic Functions
|
lecturing, discussing, problem solving |
7 |
Ch 4: More Applications of Differentiation
4.1 Related Rates
4.3 Indeterminate Forms
4.4 Extreme Values
|
lecturing, discussing, problem solving |
8 |
Midterm |
lecturing, discussing, problem solving |
9 |
4.5 Concavity and Inflections
4.6 Sketching the Graph of a Function
|
lecturing, discussing, problem solving |
10 |
4.8 Extreme-Value Problems
4.9 Linear Approximations
|
lecturing, discussing, problem solving |
11 |
Ch 5: Integration
5.1 Sums and Sigma Notation
5.2 Areas as Limits of Sums
5.3 The Definite Integral
5.4 Properties of the Definite Integral
|
lecturing, discussing, problem solving |
12 |
5.5 The Fundamental Theorem of Calculus
5.6 The Method of Substitution
5.7 Areas of Plane Regions
|
lecturing, discussing, problem solving |
13 |
Ch 6: Techniques of Integration
6.1 Integration by Parts
6.2 Integrals of Rational Functions
|
lecturing, discussing, problem solving |
14 |
6.3 Inverse Substitutions
6.5 Improper Integrals
|
lecturing, discussing, problem solving |
15 |
Ch 7: Applications of Integration
7.1 Volumes by Slicing—Solids of Revolution
7.2 More Volumes by Slicing
7.3 Arc Length and Surface Area
|
|
16 |
Final Exam |
|
# |
Learning Outcomes |
Program Outcomes |
Method of Assessment |
1 |
Students will be able to compute limits and to carry out some basic proofs about limits and continuty. |
1͵7 |
1͵2 |
2 |
Students will be able to compute derivates and to use it in applications such as computing rates of change, finding extreme values. |
1͵7 |
1͵2 |
3 |
Students will be able to sketch graphs of functions by finding intervals of increase /decrease, concavity and asymptotes. |
1͵7 |
1͵2 |
4 |
Students will be able to use transcendental functions including logarithms, exponentials and inverse trigonometric functions effectively. |
1͵7 |
1͵2 |
5 |
Students will be able to compute integrals by the Riemann Sum defintion and use it to make approximations. |
1͵7 |
1͵2 |
6 |
Students will be able to make use of various techniques to compute proper and improper integrals. |
1͵7 |
1͵2 |