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Introductory Topics in Mathematical Techniques: Derivatives and Integrals Review

This lesson covers essential mathematical techniques for understanding basic derivatives and integrals, with a focus on partial derivatives and thermodynamic notation. Students will review concepts related to differentials and perform various calculations, including specified integrals and derivatives. Exercises will involve manipulation of mathematical expressions such as areas expressed as functions of two of four dimensions. This foundational knowledge is crucial for further studies in chemistry and related fields. Assignments are to be submitted via email by Thursday.

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Introductory Topics in Mathematical Techniques: Derivatives and Integrals Review

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  1. CHEM 433 – 9/7/11 I. Introductory Topics A. Mathematical Techniques (RIED) - Review basic derivatives & Integrals - “Partial” derivatives / “Thermo” notation - “Differentials” and manipulations thereof Read: A2.4, A2.6 and “REID” HW: via e-mail Thursday …

  2. Do these integrals (these eliminate the “+C” part): 1/2 x2 1/3 x3– x ln x Do these derivatives: 2e2x 4x -2x–3

  3. Do these partial derivatives for: 2x 3y2 2 6y 0

  4. Reid’s evil rectangle: This illustrates how “A” (area) can be a function of any 2 of the 4 dimensions (variables). A is a 2-D function any way you slice it ! t s h b

  5. If we regard A as a function of b & h (i.e. A(b,h)), what is the general expression for the differential of A: >>> dA = ?

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