Calculus III
Calculus III
Required or Elective: Mandatory for all Engineering and IT students.
Course Prerequisites: 31133 Calculus II
Catalog Description:
Three Dimensional Coordinate System, Vectors, Dot and Cross Products, Lines and Planes in Space, Cylindrical and Quadric Surfaces, Curves in Space and Their Tangents, Integral of Vector Functions, Arc Length in Space, Curvature and Normal vectors of A Curve, Tangential and Normal Components of Acceleration, Velocity and Acceleration in Polar Coordinates, Functions of Several Variables, Limits and Continuity in Higher Dimensions, Partial and Directional Derivatives, Chain Rule, Gradient Vector, Tangent planes and Normal lines of Surfaces in Space, Differentials, Extreme values and Saddle Points, Lagrange Multipliers, Double Integrals in Cartesian and Polar Coordinates, Triple integrals in Cartesian, Cylindrical and Spherical Coordinates.
Textbook and Related Course Materials:
- Textbook: Calculus: Early Transcendentals, Metric Edition , 9th Edition (Stewart- Cengage)
Topics covered and level of coverage:
Vectors and the Geometry of Space. 11 hrs
Vector-Valued Functions and Motion in Space. 11 hrs
Partial Derivatives. 14 hrs
Multiple Integral. 12 hrs
Course learning outcomes (CLOs):
llustrate the vector concept and perform vector operations.
Recognize and identify equations of lines, planes, and Quadratic surfaces, and describe the properties of these geometric beings.
Calculate the length, the curvature, the tangent, and normal vectors for a given curve in space or plane and recognize the notion of smooth curves.
Describe and sketch the domain of a function of several variables and solve its limits in several coordinate systems.
Calculate the partial derivative, gradient vector, and directional derivatives of a function of several variables.
Evaluate double and triple integrals in several coordinate systems.
Contribution to the Professional Component: Mathematics & Basic Sciences (100 %).
Expected Level of Proficiency for Students Entering the Course: Mathematics (High), Computer programming (Very Low).
Will this course involve computer assignments? Yes
Will this course have TA(s) when it is offered? Yes.
Level of contribution to program outcomes:
Strong: 1
Average: 3,5,7
Weak: -
ABET’s course outcomes (a-k) criteria
Engineering programs must demonstrate that their graduates have:
an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. an ability to communicate effectively with a range of audiences.
4. an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Chapter 12: Vectors and the Geometry of Space
Chapter 13: Vector Functions
Chapter 14: Partial Derivatives
Chapter 15: Multiple Integrals
Problem solving: The plane equation. PARTT I
Problem solving: Maximum and Minimum values 14. 7 PART I
Problem solving: Triple integrals in cylindrical coordinates
Course code (for online HW and material). Section 1 (11-12): psut.jo81841201
Course code (for online HW and material). Section 2 (9:30-11): psut.jo85155869
Section 1 (11-12): https://www.cengage.com/coursepages/PSUT_Calculus_3_Dr_Mohammed_Section_01_Fall23
Section 2 (9:30-11): https://www.cengage.com/coursepages/PSUT_Calculus_3_Dr_Mohammed_Section_02_Fall23
1- Group work of up to 4 students is allowed. In fact, having a group work is better than individuals; it is one goal of the projects to work together.
2- The questions that I pose on each project are not the only thing you can do. These are kind of the main ideas. However, you will have your other good ideas which you can strengthen your project by.
3- When you prepare your project, make sure to answer the questions that are asked clearly and in a good way that makes it easy for the reader to follow.
4- You will need to submit a report and a presentation for your project. The report is a word (pdf) file that addresses all questions; as if you are writing a "book" about the project. The presentation should be prepared using power point tool, for example, in a way that summarizes your project. In presentations, make sure to have minimal writing. Graphics and animations are way better in presentations than text.
5- After finishing your report and presentation and submitting them, your report and presentation will be graded, and you will be given partial credit.
6- The final grade will depend on your presentation.
7- The presentation will be face-to-face in university.
8- In the presentation, every member of the group should present his contribution and defend it.
9- I will invite people from outside the class to attend your presentations and to participate in grading the projects.
10- You need to remember some stuff: We really trust you all. I will not ask anyone if he/she has copied from someone else, or if someone else has done the project for you. PSUT students are trustworthy, and I will not question your loyalty and honesty.
These projects may take some effort and time from you, but it will help you better understand the topic and will qualify you for future courses. In engineering, project based courses are trending these days.
11- Of course, you will have to work on one project only.
12- Projects must be finished at least 2 weeks before the end of the semester so that we have sufficient time to grade and present them.
13- These are general guidelines that you will need to follow. I will add further guidelines if needed later.
Course code (for use with cengage HW): psut.jo 1292 9359