Can I get the answers for these two computational physics problems?

Book suggestions:

? "Computational Physics" by Mark Newman (guide to Python in computational physics)

? "Numerical Recipes" by W. H. Press et al. (covers very comprehensibly a vast range of numerical topics; 3rd edition is in C++; older editions, e.g. in C, are freely available online)

? "Clean Code" by Robert C. Martin (great book on good programming practices)

Problem 1: Bisection method

Planck's radiation law tells us that the intensity of radiation per unit area and per unit wavelength A from a black body at temperature 7 is 2The2X 5 I (A) = ehc /AkBT _ where h is Planck's constant, c is the speed of light, and kg is Boltzmann's constant. a) Show by setting the derivative of I(A) to zero that the wavelength A at which the emitted radiation is strongest is the solution of the equation 5ehc/AkBT 5 = 0. AKBT b) Make the substitution I = hc/AkgT' and hence show that the wavelength of maximum radiation obeys the Wien displacement law: 10 T where the so-called Wien displacement constant is b = he/kga, and a is the solution to the nonlinear equation 5e ? +x -5 =0. c) Plot the left hand side of this equation. You will see that there are two roots, but only one of them is physical. Which one and why? d) Write a program to solve this equation to an accuracy of e = 10-6 using the bisection method, and hence find a value for the displacement constant. You can either use a library or implement bisection directly. e) The displacement law is the basis for the method of optical pyrometry, a method for measuring the temperatures of objects by observing the color of the thermal radiation they emit. The method is commonly used to estimate the surface temperatures of astro- nomical bodies, such as the Sun. The wavelength peak in the Sun's emitted radiation falls at A = 502 nm. From the equations above and your value of the displacement constant, estimate the surface temperature of the Sun.In a previous homework we considered circuits of resistors. Resistors are linear (current is proportional to voltage) and the resulting equations are therefore also linear and can be solved by standard matrix methods. Real circuits, however, often include nonlinear components and require solving nonlinear equations. Consider the following simple circuit, a variation on the classic Wheatstone bridge: VA R1 R 3 W V1 V 2 R2 RA 0 The resistors obey the normal Ohm law, but the diode obeys the diode equation: 1 = Jo(e /T - 1), where V is the voltage across the diode and lo and Vr are constants. a) Applying the Kirchhoff current law to voltage Vi in the circuit above we get V1 - V+ , VL + 10[e(-V2)/V - 1] =0. R2 Derive the corresponding equation for voltage V2. b) Implement Newton's method from scratch to solve the two nonlinear equations for the voltages V, and lo with the conditions V. - 5V. R, - 1KS, R2 = 4 ks, R3 - 3k0, R. - 2ks2, 40 = 3nA, V7 = 0.05 V c) The electronic engineer's rule of thumb for diodes is that the voltage across a (forward biased) diode is always about 0.6 volts. Confirm that your results agree with this rule