Differential and Integral Calculus(高数).docx

Differential and Integral CalculusCourse Content and Basic RequirementsCourse contents: Limits and continuity; the calculus of functions of one variable; ordinary differential equation; vector algebra and analytic geometry of space; multi-function calculus; infinite series.(II) Course teaching content and Knowledge Part Arrangement1. Knowledge Unit One: The Function & The Limit (15 hours)(1) Knowledge point 1: Mapping and mapping(2) Knowledge point 2: The limit of series(3) Knowledge point 3: The limit of function(4) Knowledge point 4: Infinitesimal and Infinite(5) knowledge point 5: The limit algorithm(6) Knowledge point 6: Limit existing criteriaTwo important limits(7) Knowledge point 7: Comparison of Infinitesimals (8) knowledge point 8: Continuity and discontinuous point of the function(9) knowledge point 9: Operation properties of continuous function & Continuity of elementary functions(10) knowledge points 10: Property of continuous function on closed interval2. Knowledge Unit Two: Derivative and Differential (10 hours)(1) Knowledge point 1: The concept of Derivative(2) Knowledge point 2: Derivative rule of the function(3) Knowledge point 3: Derivative of higher order (4) Knowledge point 4: The derivative of the function determined by Implicit functions and Parametric equation (5) Knowledge point 5: Differential of the function3. Knowledge Unit Three: Differential Mean Value Theorem and the Applications of Derivatives (10 hours)(1) Knowledge point 1: Differential Mean Value Theorem(2) Knowledge point 2: Hospital Rule(3) Knowledge point 3: Taylor Formula(4) Knowledge point 4: Monotonicity and Concavity of the function(5) Knowledge point 5: Extremum, Maximum and Minimum of the function(6) Knowledge point 6: Delineation of function graphic(7) Knowledge point 7: Curvature4. Knowledge Unit Four: Indefinite Integral (hours 10)(1) Knowledge point 1: Concepts and Properties of the Indefinite Integral(2) knowledge point 2: Integral by Substitution(3) Knowledge point 3: Integral by Parts(4) knowledge point 4: Integration of Rational Function5. Knowledge Unit Five: Definite integral (10 hours)(1) Knowledge point 1: Concepts and Properties of the Definite Integral(2) knowledge point 2: Fundamental Theorem of Calculus (3) Knowledge point 3: Integral by Substitution and Integral by Parts of Definite Integral(4) Knowledge point 4: Improper Integral6. Knowledge Unit Six: Application of definite integral (3 hours)(1) Knowledge point 1: element method of definite integral (2) Knowledge point 2: the application of definite integral in geometry(3) Knowledge point 3: the application of definite integral in physics7. Knowledge Unit Seven: Space analytic geometry and Vector algebra (12 hours)(1) Knowledge point 1: vector and its linear operator(2) knowledge point 2: Dot product Vector product(3) Knowledge point 3: Curved surface and its equation(4) Knowledge point 4: Space curve and its equation(5) knowledge point 5: Plane and its equation(6) Knowledge point 6: Spatial line and its equation 8. Knowledge Unit Eight: multi-function differential method and its application (16 hours)(1) Knowledge point 1: Basic concepts of Multi-function(2) knowledge point 2: partial derivative(3) Knowledge point 3: total differential(4) knowledge point 4: derivative rule of composite multi-function (5) knowledge point 5: derivation formula of implicit function (6) Knowledge point 6: geometric applications of multi-function differential calculus (7) Knowledge point 7: Directional Derivatives and Gradient(8) knowledge point 8: Extremum of multi-function and its Method9. Knowledge Unit Nine: Double Integral (8 hours)(1) Knowledge point 1: concept and property of Double Integral(2) Knowledge point 2: calculation method of double integral (3) knowledge point 3: triple integral(4) Knowledge point 4: application of triple integral10. Knowledge of Unit Ten: curve integrals and surface integrals (20 hours)(1) Knowledge point 1: curve integral of arc length (2) Knowledge point 2: curve integral of coordinates(3) knowledge point 3: The green Formula and its applications(4) Knowledge point 4: surface integrals of area (5) knowledge point 5: surface integrals of coordinates(6) knowledge point 6: Gaussian formulaStokes formula11. Knowledge Unit Eleven: Infinite Series (17 hours)(1) Knowledge point 1: concept and property of Constant series(2) knowledge point 2: inspecting convergent of constant series (3) Knowledge point 3: Power Series(4) Knowledge point 4: function expansion into power series(5) knowledge point 5: applications of the power series expansion function(6) Knowledge point 6: Fourier series12. Knowledge Unit Twelve: Differential Equations (13 hours)(1) Knowledge point 1: basic concepts of Differential Equations(2) Knowledge point 2: differential equation of separable variables (3) Knowledge point 3: homogeneous equation(4) Knowledge point 4: first order linear differential equations(5) Knowledge point 5: total Differential Equations(6) Knowledge point 6: reducible high order differential equations(7) Knowledge point 7: High Order linear Differential Equations(8) Knowledge point 8: constant coefficient homogeneous linear differential equation (9) Knowledge point 9: constant coefficient fly homogeneous linear differential equationTotal class hours 160, include lecture class 114 hours, exercise class 30 hours, flexible 16 hoursClass Hours Associate SheetCourse contentRecommend class hoursTeachingLectureExerciseFlexibleSubtotal1. Limit and continuous of function123152. Derivatives