MAT A35 ( Calculus for the Life Sciences II)
LW1. Preview. Integration. Techniques of Integration.
Techniques of Integration (Partial fractions decomposition and Integration by Parts)
LW2. Improper Integrals. Numerical Integration.
Application: Volumes, Areas.
Improper integrals (Type 1: Unbounded intervals. Type 2: Discontinuous integrand). Examples.
Application to Physics, Economics and Biology.
Matrix operations. Systems of linear equations. Applications: Leslie Diagram & Matrix.
Inverse matrix and cofactor expansions. Applications: Population models
LW4. Eigenvalues and Eigenvectors.
Computing Eigenvectors and Eigenvalues. Applications: Population Growth & Long – Term
LW5. Functions of several Variables. Multiple integration.
Partial derivatives. Maximum – minimum problems. Applications: Body Surface Area, Wind
Speed of Tornado, Optimization Problems.
LW6. Elements of Regression analysis.
Method of least squares. Best fit line. Quadratic, Exponential and Power dependences.
Application: Experimental Data Fitting (Project)
LW7. Separable and Linear First Order Differential Equations.
Pure time and autonomous differential equations.
Integrals as General and Particular Solutions. Direction fields and solution curves. Phase line.
Substitution methods. Bernoulli equation. Applications: General population Model. Logistic
Model. Carrying Capacity of Population.
LW8. Differential equations and mathematical modeling
Mixture problems. One and Two -Compartment models. Applications: Pollution of Great Lakes,
Crop Yield, Mixing Chemicals.
LW9. Higher- Order Differential Equations. Numerical Solutions.
Second Order Differential Equations with constant Coefficients. Homogeneous and non-
Applications: Mechanical and Electrical Vibrations, Parallel Reactions.
LW10. Systems of Autonomous Differential Equations and Stability.
Autonomous Equations. Equilibrium Solution. Qualitative Analysis.
Applications: Logistic Growth Model with a Threshold, Crystallization, Decay Rate, Plant
LW11. Power Series Expantion.
Taylor Series. Series representation of functions: linear and quadratic approximation.
LW12 Systems of Nonlinear Differential Equations.
Linearization. Applications: Population models. Predator-Prey & Coexistence of Species