By the end of the course, the students will be able to

• implement all the numerical methods studied using MATLAB

In Calculus:

• identify whether a given formula is a function or not
• determine the inverse of a function if exists
• draw a function of a single or more variables and common graphs
• draw and solve basic trigonometric, exponential and logarithmic functions
• evaluate basic limits
• define the formal meaning of continuity and differentiability
• calculate the derivatives of a function by analytic and numerical methods
• solve implicit differentiation problems
• find the roots and critical points (minimum and maximum points) of a function by using analytical and numerical techniques
• find the linear or higher order approximation of a function
• evaluate basic single and double integrals

In Linear algebra:

• translate a verbal statement of variables in the form of a linear equations
• formulate and solve a system of linear equations
• calculate the determinant and inverse of a matrix
• define a vector and a subspaces
• prove basic linear algebra properties and equations
• find the Eigenvalues and Eigenvectors of a square matrix
• formulate and solve basic least square problems (quadratic optimization)
• solve a quadratic optimization problem using basic iterative methods (steepest descent, conjugate gradient, etc)

In Differential Equations:

• classify and interpret differential equations
• solve first order linear, separable and exact differential equations analytically