Calculus for CENV Technology MATH 2416

Upon successful completion, the student will be able to:

• Understand the meaning of the first derivative as the instantaneous rate of change of a function. Example applications:
• Discuss the concept of reaction order in chemical kinetics.
• Determine instantaneous reaction rates for various problems and compare these results to the average rate of change.
• Differentiate functions commonly encountered in chemistry including trigonometric, logarithmic and exponential functions.
• Apply the first and second derivative test in order to find local maxima and minima.
• Apply the maximum and minimum concept to problems in chemical and environmental technology.
• Understand the meaning of the indefinite integral as the inverse operation of differentiation and apply this concept to chemical and environmental problems.
• Integrate functions commonly encountered in chemistry including trigonometric, logarithmic and exponential functions.
• Understand the meaning of the definite integral as the area under a curve and the mean value of a function.
• Apply the definite integral to practical chemical and environmental problems. Example applications:
• Calculate work as related to pressure and volume in thermodynamic systems.
• Determine enthalpy and entropy when molar heat capacity is expressed as a function of absolute temperature.
• Solve integrals using Numerical Methods in Excel, e.g. Linear Interpolation and Newton-Raphson Methods
• Solve applied problems involving first order linear differential equations. Examples include rates of chemical reactions, mixing of solutions and Newton’s Law of Cooling
• Solve differential equations using Numerical Methods in Excel, e.g. Euler’s and Modified Euler’s Methods
• Propagate error through algebraic and transcendental formulas (calculus method). Example application:
• General analysis of experimental data and associated calculations.

Effective as of Winter 2027