This is a 4 credit course intended for freshman students persuing a degree in Computer Science and Engineering. The goal of this course is to build a solid foundation in differecial canculus, 2D and 3D geometry for engineering studetns. My goal as the instructor was to present course contects in an intuitive manner and to connect the materials taught with various applications in the field of Computer Science.

Syllabus and Course outline:

• Change of axes: transformation of coordinates, Simplification of equations of the curve
• Pair of straight lines:Homogeneous second-degree equations, Conditions for general second-degree equations to represent a pair of straight lines, angle between the lines, Pair of straight lines joining the origin to the points of intersection of the curve and a line.
• Real numbers, Number line, Intervals ,Function, Domain and Range of functions, Shifting Graphs, Rates of Change and Tangents to Curves, Limit of a function
• Precise Definition of a limit, One Sided Limits, Continuity
• Tangents and derivative at a point, Derivative as a function, Differentiation rules
• Derivative as a rate of change
• Trigonometric Derivatives
• The chain rule
• Implicit Differentiation
• Derivative of Inverse functions and Logarithms, Inverse Trigonometric Functions
• Linearization and Differentials
• Maximum and minimum values of functions and points of inflection
• Rolle's Theorem, Mean Value Theorem
• Monotonic function and 1st derivative test for finding maximums and miniums
• Concavity and 1st, 2nd derivative tests to determine concavity
• Curve sketching from concavity
• Indeterminant form and L hospitals rule
• Applied optimization
• Taylor's theorem and Mclaurin's theorem
• Application of Derivatives