BSc in Mechanical Engineering

Course Information Package

Course Unit TitleCALCULUS AND ANALYTIC GEOMETRY II
Course Unit CodeAMAT122
Course Unit DetailsBSc Automotive Engineering (Required Courses) - BSc Mechanical Engineering (Required Courses) - BSc Civil Engineering (Required Courses) - BSc Quantity Surveying (Required Courses) - BSc Electrical Engineering (Required Courses) - BSc Computer Engineering (Required Courses) - BSc Computer Science (Required Courses) -
Number of ECTS credits allocated5
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
  1. Explain the notion of definite and indefinite integrals, state and use the Fundamental Theorem of Calculus.
  2. Solve simple definite and indefinite integrals of polynomials, functions involving rational powers of the variable, exponential, trigonometric, and rational functions.
  3. Solve more complicated integrals by using the methods of integration by parts, u-substitution, partial fraction decomposition, and trigonometric substitution.
  4. Explain the concept of functions of two variables, find partial derivatives,
  5. Explain the concept of infinite series, state Taylor’s and MacLaurin’s Theorems, and expand simple functions in such series.
  6. Explain the notion of complex numbers, evaluate simple expressions involving complex numbers, and express complex numbers in polar form.
  7. Apply definite integration in order to compute areas between curves, and volumes of solids of revolution by using the methods of slices and cylindrical shells.
Mode of DeliveryFace-to-face
PrerequisitesAMAT111Co-requisitesNONE
Recommended optional program componentsNONE
Course Contents

Definite and Indefinite integrals: The notions of definite and indefinite integrals. Fundamental Theorem of Calculus.

Applications of the Definite Integral: Areas between two curves, volumes by the methods of slices and cylindrical shells, and areas of surfaces of revolution.

Techniques of Integration: Method of u-substitution, Integration by Parts, partial fraction decomposition. Trigonometric integrals, inverse trigonometric and hyperbolic functions:  their derivatives and integrals, integrals of powers of sines, cosines, tangents and secants by using reduction formulae, trigonometric substitutions.

Introduction to Partial Derivatives and Double Integrals.

Series: Infinite series, Power Series, Taylor and MacLaurin Series, tests of convergence.

Polar Coordinates: Polar coordinates and conversion of Cartesian to Polar coordinates. Areas in polar coordinates.

An introduction to complex numbers: Geometric interpretation, Polar form, Exponential form, powers and roots.

Recommended and/or required reading:
Textbooks
  • Anton H., Bivens I and Davis S, Calculus, 7th edition, John Wiley & Sons, 2002.
References
  • C. Henry Edwards, David E. Penney, Calculus, Matrix Version, Pearson Education; 6th edition, 2002.
  • James Stewart, Calculus, Concepts and Context, Thomson Learning; 3rd Bk & CD edition, 2004.
Planned learning activities and teaching methods

The theory is taught and several examples are solved on the white board.         

Students are encouraged to participate.

Technology is used to deliver concepts and ideas.

Students are asked to work on their own during class hours on examples and practice problems.

Extra homework is given to students to work at home.

Students are encouraged to attend office hours for extra help.

Assessment methods and criteria
Tests40%
Final Exam60%
Language of instructionEnglish
Work placement(s)NO