MATH 2E PREVIOUS LECTURES     

W9-F: Oriented surfaces. Surface integral of a vector field.    
W9-W: Integral of a function over a surface. Special cases: Area of a surface, surface which is a graph of a function. Applications: computing mass from density, electric charge from density of electric charge, center of gravity.  
W9-M: Examples of parametrized surfaces. Grid lines. Tangent planes. Smooth surfaces. Introduction to surface integrals.   

W8-F: Laplace operator. 2-dimensional variants of Stokes and divergence theorem. Parametrized surfaces, grid lines (Section 16.6)  
W8-W: Review of cross (vector) products. Curl and divergence (Section 16.5) 
W8-M: Criterion in conservativity of a vector field in 2D. Extended version of Green's theorem. Line integrals along closed curves of vector fields with singularities.    

W7-F: Conservative fields and path independence. Green's Theorem (Section 16.4) 
W7-W: Midterm 2   
W7-M: Holiday       

W6-F: Integrating along closed curves. Path independence and conservative vector fields. 
W6-W: Fundamental theorem for line integrals, criterion on conservativity of a vector field, computation of the potential function of a conservative vector field (Section 16.3)
W6-M: Curve orientation, Line integral of a vector field  (Section 16.2)    

W5-F: Applications of the integral of a function with respect to arc length: mass, moments, center of gravity. Orientation of a curve.  
W5-W: Integral of a function with respect to the arc length, Section 16.2  
W5-M: Vector fields, Section 16.1  

W4-F: Review of verctor algebra. Vector fields, Section 16.1.   
W4-W: Change of coordinates III: Examples in 2D: polar transformation, "stretched" polar transformation -- area of an ellipse, linear transformation. Change of coordinates in 3D: general formula and the Jacobian.  
W4-M: Midterm 1

W3-F: Change of coordinates Part II, Section 15.10   
W3-W: Change of coordinates Part I, Section 15.10     
W3-M: Holiday

W2-F: Discussion - problem solving    
W2-W: Section 15.9: Triple integrals in spherical coordinates.    
W2-M: Discussion - problem solving     

W1-F: Section 15.4: Area of a region in polar coordinaltes. Section 15.7: Triple integrals and Section 15.8: Triple integrals in cylindrical coordinates.    
W1-W: Section 15.3: Picking the suitable type for the region to make integration simple. 15.4: Double integrals in polar coordinates. Volume of a ball.    
W1-M: Sections 15.1 - 15.3: Review of double integrals    

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