## MAT 104: Calculus and Analytical Geometry

3 credits. Prerequisites: none.

### Course rationale

This is one of the General Education courses offered by the university, which fulfills the requirement of foundation in “Numeracy”. This course is mandatory for the students who wish to major in Computer Science and Engineering. Preliminary theories of calculus will be reviewed with analytical geometry.

### Course content

Functions: introduction, domain, range, new functions from old (algebraic and composite functions), even & odd functions, exponential, and logarithmic functions. Translation, reflection, and symmetry of graph of an equation. Limit: intuitive approach and computation of limit. Continuity: definition and determination of continuity of a function. Derivative function: definition as a limit, derivation of differentiation rules. Rules of differentiation: chain rule, implicit differentiation, differentiation of logarithmic functions. L’Hôpital’s rule: Indeterminate forms. Application of differentiation: analysis of functions, absolute maxima, and minima, and applied maximum and minimum problems. Indefinite integrals: antiderivative, integration by substitution, integration by parts. Definite integrals: Definite integral as an area, properties of definite integral. Application of integration: calculation of area, initial value problems. Fundamental theorem of calculus: derivative of integral functions, Mean value theorem of integration, Area between two curves.

### Course objectives

1. To discuss basic theories of single variable calculus in light with analytic geometry.
2. To explain concept of limit and their evaluation where applicable.
3. Derive differentiation rules by the definition of derivative functions.
4. Relate theory with practical problems where differentiation is needed.
5. Introduce antiderivative and some techniques to calculate them.
6. Discuss use of antiderivatives to find solution of some problems.

### References

1. Anton, Bivens and Davis, Calculus (Tenth edition), Wiley Publishing Company.
2. Thomas, G.B., Finney R.L. and Weir, M.D., Calculus and Analytic Geometry (9th edition), Addition-Wesley Publishing Company.
3. Daniel kleppner and Norman Ramesy, Quick Calculus: A Self-Teaching Guide (2th edition).