To introduce the students to integral calculus and its applications.
Course Learning Outcomes:
By the end of this course the learner should be able to:-
· Apply various methods of integration on given functions
· Apply integration to calculate
· Area under graph of continuous function
· Volume of revolution surfaces
· Area of surfaces
· Length of lines and areas
· Perform numerical integration.
· State, prove and apply Taylor’s Theorem
· Apply first order p.d.e in problem solving
Methods of Integration, applications of integration, sequences and series, numerical series, convergence tests, numerical integration, Taylor’s theorem, Partial differentiation, applications. Pre-requisite: SMA121
Textbooks and Journals for the course:
- Thomas G.P. and R.L Finney (1996) Calculus and Analytic Geometry , (9th Edition) Addison-Wesley ISNB 978-0201531749
- Keith E. Hirst (2006) Calculus of one Variable, springer ISNB 9781846282225
- Serge Lang; (2012) A first Course in Calculus; springer ISNB97814612642286.
- James Stewart (2008): Calculus Early Transcendentals. Sixth edition. Brooks/ Cole, Cengage Learning, USA.
- Paul's online notes: One of the best references for the course. It has lots of worked examples as well as exercises with solutions. A very good online resource for revision of the course materials.
- William Briggs, Lyle Cochran and Bernard Gillett (2013). Calculus for Scientists and Engineers. Early Transcendentals . Pearson Education Inc., Boston
- George B. Thomas and Ross L. Finney (1996). Calculus and Analytic Geometry. Addison-Wesley Publishing Company, USA.
To introduce students to differential Calculus and to the interpretation of the derivative as a rate of change and introduce antiderivatives.
Course Learning Outcomes:
By the end of this course; the student should be able to:
· Define limits and continuity of functions
· Differentiate functions of a single variable,
· Solve problems involving parametric and implicit differentiation, anti-derivatives and give their applications to area and volume of revolution.
· Integrate functions by using substitution methods.
· Solve problems on applications of differentiation and integration.
· State and prove mean value theorems of differential calculus.
Limits and continuity of functions, differentiation of functions of a single variable, parametric and implicit differentiation, anti-derivatives and application to areas and volume of revolution, integration by substitution, by parts, by reductions and by partial fractions, maxima and minima and inflexion. applications of differentiation, mean value theorems of differential calculus.
Textbooks and Journals for this course:
· Serge Lang (2012) A first Course in Calculus ; springer ISNB 9781461264286
· Thomas G.P and R.L. Finney Calculus and Analytic Geometry (9th Edition) Addison-Wesley (1996) ISNB 978-0201531749
· Keith E. Hirst (2006) Calculus of one Variable; springer ISNB9781846282225